A. बिंदु (\left\(0,-7\right\))/Point (\left\(0,-7\right\))
Step 1
Concept
Putting (x=0) gives (-2y=14), so (y=-7). In a (y)-intercept, the (x)-coordinate is (0).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(0,-7\right\)) / Point (\left\(0,-7\right\)). Putting (x=0) gives (-2y=14), so (y=-7). In a (y)-intercept, the (x)-coordinate is (0).
Step 3
Exam Tip
(x=0) रखने पर (-2y=14), इसलिए (y=-7)। (y)-अवरोध में (x)-निर्देशांक (0) होता है।
B. बिंदु (\left\(0,-8\right\))/Point (\left\(0,-8\right\))
Step 1
Concept
Putting (x=0) gives (-3y=24), so (y=-8). Plot a negative intercept below on the (y)-axis.
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(0,-8\right\)) / Point (\left\(0,-8\right\)). Putting (x=0) gives (-3y=24), so (y=-8). Plot a negative intercept below on the (y)-axis.
Step 3
Exam Tip
(x=0) रखने पर (-3y=24), इसलिए (y=-8)। ऋण अवरोध को (y)-अक्ष पर नीचे अंकित करें।
At (y=0), (x=8), and at (x=0), (y=6). Intercepts help draw the line quickly and correctly.
Step 2
Why this answer is correct
The correct answer is A. ( (8,0) ) और ( (0,6) ) / ( (8,0) ) and ( (0,6) ). At (y=0), (x=8), and at (x=0), (y=6). Intercepts help draw the line quickly and correctly.
Step 3
Exam Tip
(y=0) पर (x=8) और (x=0) पर (y=6)। अवरोधों से रेखा जल्दी और सही बनती है।
At (y=0), (x=8), and at (x=0), (y=6). Write the (x)-intercept first and then the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is A. ( (8,0) ) और ( (0,6) ) / ( (8,0) ) and ( (0,6) ). At (y=0), (x=8), and at (x=0), (y=6). Write the (x)-intercept first and then the (y)-intercept.
Step 3
Exam Tip
(y=0) पर (x=8) और (x=0) पर (y=6)। पहले (x)-अवरोध और फिर (y)-अवरोध लिखें।
Putting (y=0) gives (x=4), and putting (x=0) gives (y=-3). Intercepts help draw the line quickly.
Step 2
Why this answer is correct
The correct answer is A. ((4,0)) और ((0,-3)) / ((4,0)) and ((0,-3)). Putting (y=0) gives (x=4), and putting (x=0) gives (y=-3). Intercepts help draw the line quickly.
Step 3
Exam Tip
(y=0) रखने पर (x=4) और (x=0) रखने पर (y=-3)। अवरोधों से रेखा जल्दी खींची जा सकती है।
A. बिंदु (\left\(4,0\right\))/Point (\left\(4,0\right\))
Step 1
Concept
Putting (y=0) gives (5x=20), so (x=4). In an (x)-intercept, the (y)-coordinate is (0).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(4,0\right\)) / Point (\left\(4,0\right\)). Putting (y=0) gives (5x=20), so (x=4). In an (x)-intercept, the (y)-coordinate is (0).
Step 3
Exam Tip
(y=0) रखने पर (5x=20), इसलिए (x=4)। (x)-अवरोध में (y)-निर्देशांक (0) होता है।
A. इससे शून्यक निश्चित नहीं होता/A zero cannot be determined from this alone
Step 1
Concept
The (y)-intercept tells (p(0)) not all zeroes. Zeroes need (x)-axis intersections.
Step 2
Why this answer is correct
The correct answer is A. इससे शून्यक निश्चित नहीं होता / A zero cannot be determined from this alone. The (y)-intercept tells (p(0)) not all zeroes. Zeroes need (x)-axis intersections.
Step 3
Exam Tip
(y)-प्रतिच्छेद (p(0)) बताता है न कि सभी शून्यक। शून्यक के लिए (x)-अक्ष से प्रतिच्छेद चाहिए।
The point ((0,0)) lies on both the (y)-axis and the (x)-axis. Tip: the origin is common to both axes.
Step 2
Why this answer is correct
The correct answer is A. (0) भी शून्यक है / (0) is also a zero. The point ((0,0)) lies on both the (y)-axis and the (x)-axis. Tip: the origin is common to both axes.
Step 3
Exam Tip
((0,0)) (y)-अक्ष और (x)-अक्ष दोनों पर है। टिप: मूल बिंदु दोनों अक्षों का साझा बिंदु है।
For (0) to be a zero (p(0)) must be (0). Tip: a (y)-axis intercept is not always a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं क्योंकि (p(0)=5) / No because (p(0)=5). For (0) to be a zero (p(0)) must be (0). Tip: a (y)-axis intercept is not always a zero.
Step 3
Exam Tip
शून्यक के लिए (p(0)) को (0) होना चाहिए। टिप: (y)-अक्ष कटान हमेशा शून्यक नहीं होता।
A. बिंदु (\left\(0,-5\right\))/Point (\left\(0,-5\right\))
Step 1
Concept
Substituting (\left\(0,-5\right\)) gives (5\left\(0\right\)-6\left\(-5\right\)=30). A negative (y)-intercept is plotted downward on the graph.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(0,-5\right\)) / Point (\left\(0,-5\right\)). Substituting (\left\(0,-5\right\)) gives (5\left\(0\right\)-6\left\(-5\right\)=30). A negative (y)-intercept is plotted downward on the graph.
Step 3
Exam Tip
(\left\(0,-5\right\)) रखने पर (5\left\(0\right\)-6\left\(-5\right\)=30)। ऋण (y)-अवरोध ग्राफ में नीचे की ओर लगाया जाता है।
A. बिंदु (\left\(0,-3\right\))/Point (\left\(0,-3\right\))
Step 1
Concept
Substituting (\left\(0,-3\right\)) gives (3\left\(0\right\)-4\left\(-3\right\)=12). A negative (y)-intercept is plotted downward on the graph.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(0,-3\right\)) / Point (\left\(0,-3\right\)). Substituting (\left\(0,-3\right\)) gives (3\left\(0\right\)-4\left\(-3\right\)=12). A negative (y)-intercept is plotted downward on the graph.
Step 3
Exam Tip
(\left\(0,-3\right\)) रखने पर (3\left\(0\right\)-4\left\(-3\right\)=12)। ऋण (y)-अवरोध ग्राफ में नीचे की ओर लगाया जाता है।
A. क्योंकि शून्यक के लिए (y=0) चाहिए/Because a zero needs (y=0)
Step 1
Concept
Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0). Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 3
Exam Tip
शून्यक (x)-अक्ष से जुड़े होते हैं जहाँ (y=0) होता है। (y)-अक्ष से कटाव केवल (x=0) पर बहुपद का मान बताता है।
Putting (y=0) gives (x=4), and putting (x=0) gives (y=-9). Intercepts give convenient points for graphing.
Step 2
Why this answer is correct
The correct answer is A. ((4,0)) और ((0,-9)) / ((4,0)) and ((0,-9)). Putting (y=0) gives (x=4), and putting (x=0) gives (y=-9). Intercepts give convenient points for graphing.
Step 3
Exam Tip
(y=0) रखने पर (x=4), और (x=0) रखने पर (y=-9)। अवरोध ग्राफ बनाने के लिए सुविधाजनक बिंदु देते हैं।
Putting (y=0) gives (x=3), and putting (x=0) gives (y=-7). Intercepts give simple and useful points for graphing.
Step 2
Why this answer is correct
The correct answer is A. ((3,0)) और ((0,-7)) / ((3,0)) and ((0,-7)). Putting (y=0) gives (x=3), and putting (x=0) gives (y=-7). Intercepts give simple and useful points for graphing.
Step 3
Exam Tip
(y=0) रखने पर (x=3), और (x=0) रखने पर (y=-7)। अवरोध ग्राफ बनाने के लिए सरल और उपयोगी बिंदु देते हैं।
Putting (y=0) gives (x=4), and putting (x=0) gives (y=-10). Intercepts make the graph quick and clear.
Step 2
Why this answer is correct
The correct answer is A. ((4,0)) और ((0,-10)) / ((4,0)) and ((0,-10)). Putting (y=0) gives (x=4), and putting (x=0) gives (y=-10). Intercepts make the graph quick and clear.
Step 3
Exam Tip
(y=0) रखने पर (x=4) और (x=0) रखने पर (y=-10)। अवरोधों से ग्राफ जल्दी और साफ बनता है।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(5/12 \ne 17/41\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (22/2=33/3) लेकिन (99/12) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(4/9 \ne 15/31\) so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(4/9 \ne 15/31\) so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(4/9 \ne 15/31\) इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (20/2=30/3) but (90/11) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (20/2=30/3) but (90/11) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (20/2=30/3) लेकिन (90/11) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(3/8 \ne 13/29\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(3/8 \ne 13/29\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(3/8 \ne 13/29\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (18/3=24/4) but (54/11) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (18/3=24/4) but (54/11) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (18/3=24/4) लेकिन (54/11) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
The second equation is (3) times the first. Therefore, both equations show the same line in the graph.
Step 2
Why this answer is correct
The correct answer is B. एक ही रेखा / Same line. The second equation is (3) times the first. Therefore, both equations show the same line in the graph.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों समीकरण ग्राफ में एक ही रेखा दिखाते हैं।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(2/5 \ne 11/19\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(2/5 \ne 11/19\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(2/5 \ne 11/19\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (14/2=21/3) but (49/8) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (14/2=21/3) but (49/8) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (14/2=21/3) लेकिन (49/8) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
If the first two ratios are equal and the third differs, the lines are parallel and distinct. Therefore, there is no common solution.
Step 2
Why this answer is correct
The correct answer is C. अलग समानांतर रेखाएं / Distinct parallel lines. If the first two ratios are equal and the third differs, the lines are parallel and distinct. Therefore, there is no common solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर और तीसरा अलग हो तो रेखाएं समानांतर और अलग होती हैं। इसलिए कोई सामान्य हल नहीं होता।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(2/5 \ne 11/19\) so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(2/5 \ne 11/19\) so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(2/5 \ne 11/19\) इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (14/2=21/3) but (49/8) is different. Therefore the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (14/2=21/3) but (49/8) is different. Therefore the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (14/2=21/3) लेकिन (49/8) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
If the first two ratios are equal and the third differs the lines are parallel and distinct. Therefore no common solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. अलग समानांतर रेखाएं / Distinct parallel lines. If the first two ratios are equal and the third differs the lines are parallel and distinct. Therefore no common solution is obtained.
Step 3
Exam Tip
पहले दो अनुपात बराबर और तीसरा अलग हो तो रेखाएं समानांतर और अलग होती हैं। इसलिए कोई सामान्य हल नहीं मिलता।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(3/7 \ne 8/13\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(3/7 \ne 8/13\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(3/7 \ne 8/13\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (10/2=15/3) but (35/9) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (10/2=15/3) but (35/9) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (10/2=15/3) लेकिन (35/9) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
Equal first two ratios give the same slope and a different third ratio keeps the lines separate. Hence, they are distinct parallel.
Step 2
Why this answer is correct
The correct answer is C. अलग समानांतर / Distinct parallel. Equal first two ratios give the same slope and a different third ratio keeps the lines separate. Hence, they are distinct parallel.
Step 3
Exam Tip
पहले दो अनुपात बराबर होने से ढाल समान होती है और तीसरा अलग होने से रेखाएं अलग रहती हैं। इसलिए वे अलग समानांतर होती हैं।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(2/5 \ne 9/11\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(2/5 \ne 9/11\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(2/5 \ne 9/11\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
C. रेखाएं अलग समानांतर हैं/Lines are distinct parallel
Step 1
Concept
Here (8/2=12/3) but (20/6) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (8/2=12/3) but (20/6) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (8/2=12/3) लेकिन (20/6) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(5/3 \ne 8/4\) so the lines will not be parallel. They will intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(5/3 \ne 8/4\) so the lines will not be parallel. They will intersect at one point.
Step 3
Exam Tip
यहां \(5/3 \ne 8/4\) इसलिए रेखाएं समानांतर नहीं होंगी। वे एक बिंदु पर कटेंगी।
Here (2/1=4/2) but (10/7) is different. Therefore the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. समानांतर अलग रेखाएं / Distinct parallel lines. Here (2/1=4/2) but (10/7) is different. Therefore the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (2/1=4/2) लेकिन (10/7) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं मिलेंगी।
The second equation is (3) times the first. Therefore both lines will appear as the same line in the graph.
Step 2
Why this answer is correct
The correct answer is B. एक ही रेखा / Same line. The second equation is (3) times the first. Therefore both lines will appear as the same line in the graph.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए ग्राफ में दोनों रेखाएं एक ही दिखाई देंगी।
One intersection point is the common solution of both equations. Therefore exactly one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. One intersection point is the common solution of both equations. Therefore exactly one unique solution is obtained.
Step 3
Exam Tip
कटने का एक बिंदु दोनों समीकरणों का सामान्य हल होता है। इसलिए केवल एक अद्वितीय हल मिलता है।
When all three ratios are equal both equations make the same line. This situation has infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. एक ही रेखा / Same line. When all three ratios are equal both equations make the same line. This situation has infinitely many solutions.
Step 3
Exam Tip
तीनों अनुपात बराबर होने पर दोनों समीकरण एक ही रेखा बनाते हैं। ऐसी स्थिति में अनंत हल होते हैं।
C. एक बिंदु पर कटती रेखाएं/Lines intersecting at one point
Step 1
Concept
Here \(4/8 \ne 7/13\) so the slopes are different. Lines with different slopes intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(4/8 \ne 7/13\) so the slopes are different. Lines with different slopes intersect at one point.
Step 3
Exam Tip
यहां \(4/8 \ne 7/13\) इसलिए ढालें अलग हैं। अलग ढाल वाली रेखाएं एक बिंदु पर कटती हैं।
Here (2/6=1/3) but (4/10) is different so the lines are parallel. Such lines never meet.
Step 2
Why this answer is correct
The correct answer is C. समानांतर अलग रेखाएं / Distinct parallel lines. Here (2/6=1/3) but (4/10) is different so the lines are parallel. Such lines never meet.
Step 3
Exam Tip
यहां (2/6=1/3) लेकिन (4/10) अलग है इसलिए रेखाएं समानांतर हैं। ऐसी रेखाएं कभी नहीं मिलतीं।
One common point gives one unique solution. Therefore it is a consistent and independent pair.
Step 2
Why this answer is correct
The correct answer is A. संगत और स्वतंत्र / Consistent and independent. One common point gives one unique solution. Therefore it is a consistent and independent pair.
Step 3
Exam Tip
एक सामान्य बिंदु होने से एक अद्वितीय हल मिलता है। इसलिए यह संगत और स्वतंत्र युग्म है।
Completely overlapping lines are coincident. Every point on them satisfies both equations.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. Completely overlapping lines are coincident. Every point on them satisfies both equations.
Step 3
Exam Tip
पूरी तरह मिलने वाली रेखाएं संपाती होती हैं। उनके प्रत्येक बिंदु से दोनों समीकरण संतुष्ट होते हैं।
(2/4=3/6) but (6/15) is different, so the lines are parallel. Such a graph has no intersection.
Step 2
Why this answer is correct
The correct answer is C. अलग समानांतर रेखाएं / Distinct parallel lines. (2/4=3/6) but (6/15) is different, so the lines are parallel. Such a graph has no intersection.
Step 3
Exam Tip
(2/4=3/6) लेकिन (6/15) अलग है, इसलिए रेखाएं समानांतर हैं। ऐसे ग्राफ में कोई intersection नहीं होता।
The second equation is (2) times the first. Therefore, both will appear as the same line in the graph.
Step 2
Why this answer is correct
The correct answer is C. एक ही रेखा / Same line. The second equation is (2) times the first. Therefore, both will appear as the same line in the graph.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए ग्राफ में दोनों एक ही रेखा दिखेंगी।
A. दोनों रेखाओं के प्रतिच्छेद के निर्देशांक से/From the coordinates of intersection
Step 1
Concept
The solution is obtained from the coordinates of the intersection point. Intercepts alone are not enough when a second line is given.
Step 2
Why this answer is correct
The correct answer is A. दोनों रेखाओं के प्रतिच्छेद के निर्देशांक से / From the coordinates of intersection. The solution is obtained from the coordinates of the intersection point. Intercepts alone are not enough when a second line is given.
Step 3
Exam Tip
हल प्रतिच्छेद बिंदु के निर्देशांकों से मिलता है। केवल अवरोध तब पर्याप्त नहीं जब दूसरी रेखा भी दी गई हो।
At least (2) points are enough to draw a straight line. In exams, a third point may be used for checking.
Step 2
Why this answer is correct
The correct answer is A. (2) बिंदु / (2) points. At least (2) points are enough to draw a straight line. In exams, a third point may be used for checking.
Step 3
Exam Tip
एक सीधी रेखा खींचने के लिए कम से कम (2) बिंदु पर्याप्त होते हैं। परीक्षा में तीसरा बिंदु जाँच के लिए लिया जा सकता है।
A. (x)-अक्ष के समांतर क्षैतिज रेखा/Horizontal line parallel to (x)-axis
Step 1
Concept
In (y=2), (y) is fixed and (x) can change. Hence, it is parallel to the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के समांतर क्षैतिज रेखा / Horizontal line parallel to (x)-axis. In (y=2), (y) is fixed and (x) can change. Hence, it is parallel to the (x)-axis.
Step 3
Exam Tip
(y=2) में (y) स्थिर रहता है और (x) बदल सकता है। इसलिए यह (x)-अक्ष के समांतर रेखा है।
A. (y)-अक्ष के समांतर ऊर्ध्वाधर रेखा/Vertical line parallel to (y)-axis
Step 1
Concept
In (x=3), (x) is fixed and (y) can change. Such a line is parallel to the (y)-axis.
Step 2
Why this answer is correct
The correct answer is A. (y)-अक्ष के समांतर ऊर्ध्वाधर रेखा / Vertical line parallel to (y)-axis. In (x=3), (x) is fixed and (y) can change. Such a line is parallel to the (y)-axis.
Step 3
Exam Tip
(x=3) में (x) स्थिर रहता है और (y) बदल सकता है। ऐसी रेखा (y)-अक्ष के समांतर होती है।
Every point on coincident lines satisfies both equations. In exams, call this a consistent and dependent case.
Step 2
Why this answer is correct
The correct answer is A. अनंत हल / Infinitely many solutions. Every point on coincident lines satisfies both equations. In exams, call this a consistent and dependent case.
Step 3
Exam Tip
संपाती रेखाओं के सभी बिंदु दोनों समीकरणों को संतुष्ट करते हैं। परीक्षा में इसे संगत और आश्रित स्थिति कहें।
The number of real zeroes equals the number of times the graph cuts the (x)-axis. Tip: a linear polynomial has at most one zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. The number of real zeroes equals the number of times the graph cuts the (x)-axis. Tip: a linear polynomial has at most one zero.
Step 3
Exam Tip
जितनी बार आलेख (x)-अक्ष को काटता है उतने वास्तविक शून्यक होते हैं। टिप: रैखिक बहुपद का अधिकतम एक शून्यक होता है।
The (x)-coordinate of the intersection point is (10). Therefore (10) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (10) शून्यक है / (10) is a zero. The (x)-coordinate of the intersection point is (10). Therefore (10) is a zero of the polynomial.
Step 3
Exam Tip
कटाव बिंदु का (x)-निर्देशांक (10) है। इसलिए (10) बहुपद का शून्यक है।
Zeroes are found from intersections with the (x)-axis, not the (y)-axis. So if there is no (x)-axis intersection, there are (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (0). Zeroes are found from intersections with the (x)-axis, not the (y)-axis. So if there is no (x)-axis intersection, there are (0) real zeroes.
Step 3
Exam Tip
शून्यक (x)-अक्ष से मिलने पर मिलते हैं, (y)-अक्ष से नहीं। इसलिए (x)-अक्ष से कटाव न होने पर वास्तविक शून्यक (0) होंगे।
A. नहीं, क्योंकि \(y\neq 0\) है/No, because \(y\neq 0\)
Step 1
Concept
For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\). For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (y=0) होना चाहिए। ((0,4)) में (y=4) है, इसलिए (0) शून्यक नहीं है।
A. (-5) बहुपद का शून्यक है/(-5) is a zero of the polynomial
Step 1
Concept
The (x)-value where the graph cuts the (x)-axis is the zero. Do not ignore the negative sign.
Step 2
Why this answer is correct
The correct answer is A. (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial. The (x)-value where the graph cuts the (x)-axis is the zero. Do not ignore the negative sign.
Step 3
Exam Tip
जहाँ ग्राफ (x)-अक्ष को काटता है वही (x)-मान शून्यक होता है। ऋण चिह्न को अनदेखा न करें।
Same slope and same intercept mean the same line. Therefore, such a pair has infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept mean the same line. Therefore, such a pair has infinitely many solutions.
Step 3
Exam Tip
समान ढाल और समान अवरोध का अर्थ एक ही रेखा है। इसलिए ऐसे युग्म में अनंत हल होते हैं।
Same slope and same intercept mean both lines are identical. Therefore, the pair has infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept mean both lines are identical. Therefore, the pair has infinitely many solutions.
Step 3
Exam Tip
समान ढाल और समान अवरोध का अर्थ है कि दोनों रेखाएं एक ही हैं। इसलिए युग्म के अनंत हल होते हैं।
Same slope and same intercept mean both lines are identical. Therefore, the pair is consistent and dependent.
Step 2
Why this answer is correct
The correct answer is C. संगत और आश्रित / Consistent and dependent. Same slope and same intercept mean both lines are identical. Therefore, the pair is consistent and dependent.
Step 3
Exam Tip
समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए युग्म संगत और आश्रित होता है।
Same slope and same intercept mean both lines are the same. Therefore, the pair is consistent and dependent.
Step 2
Why this answer is correct
The correct answer is C. संगत और आश्रित / Consistent and dependent. Same slope and same intercept mean both lines are the same. Therefore, the pair is consistent and dependent.
Step 3
Exam Tip
समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए युग्म संगत और आश्रित है।
Same slope and same intercept mean both lines are the same. Therefore they have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती / Coincident. Same slope and same intercept mean both lines are the same. Therefore they have infinitely many solutions.
Step 3
Exam Tip
समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए उनके अनंत हल होते हैं।
Same slope and same intercept make both lines identical. Therefore infinitely many solutions are obtained.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept make both lines identical. Therefore infinitely many solutions are obtained.
Step 3
Exam Tip
समान ढाल और समान अवरोध से दोनों रेखाएं एक ही हो जाती हैं। इसलिए अनंत हल मिलते हैं।
Same slope and same intercept make both lines identical. Therefore, they have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. संपाती रेखाएं / Coincident lines. Same slope and same intercept make both lines identical. Therefore, they have infinitely many solutions.
Step 3
Exam Tip
समान ढाल और समान अवरोध से दोनों रेखाएं एक ही होती हैं। इसलिए उनके अनंत हल होते हैं।
A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे/One that cuts the (x)-axis at ((1,0)) and ((-6,0))
Step 1
Concept
If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0)). If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 3
Exam Tip
शून्यक (1) और (-6) होने पर ग्राफ (x)-अक्ष को इन्हीं (x)-मानों पर काटेगा। इसलिए बिंदु ((1,0)) और ((-6,0)) होंगे।
Here \(x+y=\frac{7}{2}+\frac{9}{2}=\frac{16}{2}=8\). Values of (x) and (y) are read directly from the intersection point.
Step 2
Why this answer is correct
The correct answer is A. (8). Here \(x+y=\frac{7}{2}+\frac{9}{2}=\frac{16}{2}=8\). Values of (x) and (y) are read directly from the intersection point.
Step 3
Exam Tip
यहाँ \(x+y=\frac{7}{2}+\frac{9}{2}=\frac{16}{2}=8\)। प्रतिच्छेद बिंदु से (x) और (y) के मान सीधे पढ़े जाते हैं।
A. चिह्न और निर्देशांक क्रम की गलती/Error of sign and coordinate order
Step 1
Concept
In (\left\(7,-3\right\)), (x=7) and (y=-3). Reversing coordinates and changing sign makes the answer wrong.
Step 2
Why this answer is correct
The correct answer is A. चिह्न और निर्देशांक क्रम की गलती / Error of sign and coordinate order. In (\left\(7,-3\right\)), (x=7) and (y=-3). Reversing coordinates and changing sign makes the answer wrong.
Step 3
Exam Tip
बिंदु (\left\(7,-3\right\)) में (x=7) और (y=-3) है। निर्देशांक उलटने और चिह्न बदलने से उत्तर गलत हो जाता है।
C. वे समांतर और अलग हैं/They are parallel and distinct
Step 1
Concept
Dividing the second equation by (2) gives (2x+3y=15). Same left side with different constants gives parallel lines.
Step 2
Why this answer is correct
The correct answer is C. वे समांतर और अलग हैं / They are parallel and distinct. Dividing the second equation by (2) gives (2x+3y=15). Same left side with different constants gives parallel lines.
Step 3
Exam Tip
दूसरे समीकरण को (2) से भाग देने पर (2x+3y=15) मिलता है। समान बाएँ पक्ष और अलग नियतांक समांतर रेखाएँ देते हैं।
