यदि (x+y=9) और (x-y=1) की रेखाएँ मिलती हैं, तो प्रतिच्छेद बिंदु कौन-सा है?
If the lines (x+y=9) and (x-y=1) meet, what is the intersection point?
#intersection
#elimination check
#graphical solution
A ( (4,5) )
B ( (5,4) )
C ( (6,3) )
D ( (3,6) )
Explanation opens after your attempt
Correct Answer
B. ( (5,4) )
Step 1
Concept
Adding both equations gives (2x=10), so (x=5) and (y=4). On the graph this will be the intersection point.
Step 2
Why this answer is correct
The correct answer is B. ( (5,4) ). Adding both equations gives (2x=10), so (x=5) and (y=4). On the graph this will be the intersection point.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (2x=10), इसलिए (x=5) और (y=4)। ग्राफ पर यही प्रतिच्छेद बिंदु होगा।
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रेखा (x+2y=6) के लिए कौन-सा बिंदु और रेखा (2x+y=6) के लिए भी सही है?
Which point is correct for both the line (x+2y=6) and the line (2x+y=6)?
#common point
#intersection
#graphical method
A ( (1,4) )
B ( (4,1) )
C ( (2,2) )
D ( (3,3) )
Explanation opens after your attempt
Correct Answer
C. ( (2,2) )
Step 1
Concept
( (2,2) ) gives (6) in both equations. The point lying on both lines is the intersection point.
Step 2
Why this answer is correct
The correct answer is C. ( (2,2) ). ( (2,2) ) gives (6) in both equations. The point lying on both lines is the intersection point.
Step 3
Exam Tip
( (2,2) ) दोनों समीकरणों में (6) देता है। जो बिंदु दोनों रेखाओं पर हो वही प्रतिच्छेद बिंदु है।
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रेखाएँ (y=2) और (3x+y=14) का प्रतिच्छेद बिंदु क्या है?
What is the intersection point of (y=2) and (3x+y=14)?
#horizontal line
#intersection
#solution
A ( (2,4) )
B ( (4,2) )
C ( (3,2) )
D ( (2,3) )
Explanation opens after your attempt
Correct Answer
B. ( (4,2) )
Step 1
Concept
Putting (y=2) gives (3x+2=14), so (x=4). With a horizontal line, (y) is already fixed.
Step 2
Why this answer is correct
The correct answer is B. ( (4,2) ). Putting (y=2) gives (3x+2=14), so (x=4). With a horizontal line, (y) is already fixed.
Step 3
Exam Tip
(y=2) रखने पर (3x+2=14), इसलिए (x=4)। क्षैतिज रेखा के साथ (y) पहले से तय रहता है।
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रेखाएँ (x=4) और (2x+y=11) किस बिंदु पर मिलेंगी?
At which point will the lines (x=4) and (2x+y=11) meet?
#vertical line
#intersection
#graphical method
A ( (4,3) )
B ( (3,4) )
C ( (4,11) )
D ( (11,4) )
Explanation opens after your attempt
Correct Answer
A. ( (4,3) )
Step 1
Concept
Putting (x=4) gives (2(4)+y=11), so (y=3). With a vertical line, (x) is already fixed.
Step 2
Why this answer is correct
The correct answer is A. ( (4,3) ). Putting (x=4) gives (2(4)+y=11), so (y=3). With a vertical line, (x) is already fixed.
Step 3
Exam Tip
(x=4) रखने पर (2(4)+y=11), इसलिए (y=3)। ऊर्ध्वाधर रेखा के साथ हल में (x) पहले से तय रहता है।
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रेखा (2x-y=6) और (x+y=3) का हल कौन-सा है?
Which is the solution of (2x-y=6) and (x+y=3)?
#graphical solution
#axis point
#intersection
A ( (1,2) )
B ( (3,0) )
C ( (2,1) )
D ( (0,3) )
Explanation opens after your attempt
Correct Answer
B. ( (3,0) )
Step 1
Concept
At ( (3,0) ), (2(3)-0=6) and (3+0=3). The intersection point is the graphical solution.
Step 2
Why this answer is correct
The correct answer is B. ( (3,0) ). At ( (3,0) ), (2(3)-0=6) and (3+0=3). The intersection point is the graphical solution.
Step 3
Exam Tip
( (3,0) ) पर (2(3)-0=6) और (3+0=3)। प्रतिच्छेद बिंदु ही ग्राफीय हल है।
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रेखाएँ (4x-y=11) और (x+y=7) के लिए सही प्रतिच्छेद बिंदु कौन-सा है?
Which is the correct intersection point for (4x-y=11) and (x+y=7)?
#fraction coordinates
#intersection
#linear equations
A ( \left\(\frac{18}{5},\frac{17}{5}\right\) )
B ( \left\(\frac{17}{5},\frac{18}{5}\right\) )
C ( (4,3) )
D ( (3,4) )
Explanation opens after your attempt
Correct Answer
A. ( \left\(\frac{18}{5},\frac{17}{5}\right\) )
Step 1
Concept
Adding (x+y=7) and (4x-y=11) gives (5x=18). Hence \(x=\frac{18}{5}\) and \(y=\frac{17}{5}\).
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{18}{5},\frac{17}{5}\right\) ). Adding (x+y=7) and (4x-y=11) gives (5x=18). Hence \(x=\frac{18}{5}\) and \(y=\frac{17}{5}\).
Step 3
Exam Tip
(x+y=7) और (4x-y=11) जोड़ने पर (5x=18) मिलता है। इसलिए \(x=\frac{18}{5}\) और \(y=\frac{17}{5}\) है।
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रेखाएँ (x+2y=10) और (2x-y=5) ग्राफ पर किस बिंदु पर मिलती हैं?
At which point do the lines (x+2y=10) and (2x-y=5) meet on the graph?
#graphical method
#intersection
#linear equations
A ( (4,3) )
B ( (3,4) )
C ( (5,2) )
D ( (2,5) )
Explanation opens after your attempt
Correct Answer
A. ( (4,3) )
Step 1
Concept
Substituting ( (4,3) ) gives (4+2(3)=10) and (2(4)-3=5). The graphical solution is the point lying on both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (4,3) ). Substituting ( (4,3) ) gives (4+2(3)=10) and (2(4)-3=5). The graphical solution is the point lying on both lines.
Step 3
Exam Tip
( (4,3) ) रखने पर (4+2(3)=10) और (2(4)-3=5)। ग्राफीय हल वही बिंदु है जो दोनों रेखाओं पर हो।
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समीकरण (x-2y=4) और (2x-y=5) का प्रतिच्छेद बिंदु कौन-सा है?
What is the point of intersection of (x-2y=4) and (2x-y=5)?
#negative coordinates
#intersection
#graphical method
A ( (2,-1) )
B ( (-2,1) )
C ( (1,-2) )
D ( (3,-1) )
Explanation opens after your attempt
Correct Answer
A. ( (2,-1) )
Step 1
Concept
Putting ( (2,-1) ) gives (2-2(-1)=4) and (2(2)-(-1)=5). Watch signs carefully with negative coordinates.
Step 2
Why this answer is correct
The correct answer is A. ( (2,-1) ). Putting ( (2,-1) ) gives (2-2(-1)=4) and (2(2)-(-1)=5). Watch signs carefully with negative coordinates.
Step 3
Exam Tip
( (2,-1) ) रखने पर (2-2(-1)=4) और (2(2)-(-1)=5)। ऋण मान वाले बिंदुओं में चिह्न ध्यान से देखें।
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समीकरण (3x-y=7) और (x+y=5) का ग्राफीय हल कौन-सा है?
Which is the graphical solution of (3x-y=7) and (x+y=5)?
#graphical solution
#checking
#intersection
A ( (2,3) )
B ( (3,2) )
C ( (4,1) )
D ( (1,4) )
Explanation opens after your attempt
Correct Answer
B. ( (3,2) )
Step 1
Concept
At ( (3,2) ), (3(3)-2=7) and (3+2=5). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is B. ( (3,2) ). At ( (3,2) ), (3(3)-2=7) and (3+2=5). This is the common point of both lines.
Step 3
Exam Tip
( (3,2) ) पर (3(3)-2=7) और (3+2=5)। दोनों रेखाओं का सामान्य बिंदु यही है।
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रेखाएँ (2x+3y=12) और (x+y=5) ग्राफ पर किस बिंदु पर मिलती हैं?
At which point do the lines (2x+3y=12) and (x+y=5) meet on the graph?
#graphical method
#intersection
#linear equations
A ( (3,2) )
B ( (2,3) )
C ( (4,1) )
D ( (1,4) )
Explanation opens after your attempt
Correct Answer
A. ( (3,2) )
Step 1
Concept
( (3,2) ) satisfies both equations. In graphical method this intersection point is the solution.
Step 2
Why this answer is correct
The correct answer is A. ( (3,2) ). ( (3,2) ) satisfies both equations. In graphical method this intersection point is the solution.
Step 3
Exam Tip
( (3,2) ) दोनों समीकरणों को संतुष्ट करता है। ग्राफीय विधि में यही प्रतिच्छेद बिंदु हल होता है।
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समीकरण (x+3y=15) और (x+y=7) का ग्राफीय हल कौन-सा है?
Which is the graphical solution of (x+3y=15) and (x+y=7)?
#graphical solution
#intersection
#linear equations
A ( (3,4) )
B ( (4,3) )
C ( (5,2) )
D ( (6,1) )
Explanation opens after your attempt
Correct Answer
A. ( (3,4) )
Step 1
Concept
At ( (3,4) ), (3+3(4)=15) and (3+4=7). This is the intersection point of both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (3,4) ). At ( (3,4) ), (3+3(4)=15) and (3+4=7). This is the intersection point of both lines.
Step 3
Exam Tip
( (3,4) ) पर (3+3(4)=15) और (3+4=7)। यही दोनों रेखाओं का प्रतिच्छेद बिंदु है।
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रेखाएँ (x+4y=17) और (2x+4y=22) कहाँ मिलती हैं?
Where do the lines (x+4y=17) and (2x+4y=22) meet?
#graphical solution
#intersection
#linear equations
A ( (5,3) )
B ( (3,5) )
C ( (4,4) )
D ( (6,2) )
Explanation opens after your attempt
Correct Answer
A. ( (5,3) )
Step 1
Concept
At ( (5,3) ), (5+4(3)=17) and (2(5)+4(3)=22). Hence, this is the graphical solution.
Step 2
Why this answer is correct
The correct answer is A. ( (5,3) ). At ( (5,3) ), (5+4(3)=17) and (2(5)+4(3)=22). Hence, this is the graphical solution.
Step 3
Exam Tip
( (5,3) ) पर (5+4(3)=17) और (2(5)+4(3)=22)। इसलिए यह ग्राफीय हल है।
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रेखाएँ (x+2y=8) और (2x+y=10) किस बिंदु पर मिलती हैं?
At which point do the lines (x+2y=8) and (2x+y=10) meet?
#intersection
#graphical solution
#checking
A ( (2,3) )
B ( (3,2) )
C ( (4,2) )
D ( (2,4) )
Explanation opens after your attempt
Correct Answer
C. ( (4,2) )
Step 1
Concept
Substituting ( (4,2) ) gives (4+2(2)=8) and (2(4)+2=10). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is C. ( (4,2) ). Substituting ( (4,2) ) gives (4+2(2)=8) and (2(4)+2=10). This is the common point of both lines.
Step 3
Exam Tip
( (4,2) ) रखने पर (4+2(2)=8) और (2(4)+2=10)। यही दोनों रेखाओं का सामान्य बिंदु है।
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समीकरण (x+2y=11) और (x+y=7) का हल कौन-सा है?
Which is the solution of (x+2y=11) and (x+y=7)?
#graphical solution
#intersection
#checking
A ( (3,4) )
B ( (4,3) )
C ( (5,2) )
D ( (2,5) )
Explanation opens after your attempt
Correct Answer
A. ( (3,4) )
Step 1
Concept
Substituting ( (3,4) ) gives (3+2(4)=11) and (3+4=7). If both equations are satisfied, the point is the solution.
Step 2
Why this answer is correct
The correct answer is A. ( (3,4) ). Substituting ( (3,4) ) gives (3+2(4)=11) and (3+4=7). If both equations are satisfied, the point is the solution.
Step 3
Exam Tip
( (3,4) ) रखने पर (3+2(4)=11) और (3+4=7)। दोनों समीकरण संतुष्ट हों तो बिंदु हल है।
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रेखाएँ (x=4) और (y=9) किस बिंदु पर मिलेंगी?
At which point will the lines (x=4) and (y=9) meet?
#vertical horizontal lines
#intersection
#solution
A ( (9,4) )
B ( (4,9) )
C ( (4,0) )
D ( (0,9) )
Explanation opens after your attempt
Correct Answer
B. ( (4,9) )
Step 1
Concept
On the first line (x=4), and on the second line (y=9). Therefore, their common point is ( (4,9) ).
Step 2
Why this answer is correct
The correct answer is B. ( (4,9) ). On the first line (x=4), and on the second line (y=9). Therefore, their common point is ( (4,9) ).
Step 3
Exam Tip
पहली रेखा पर (x=4) और दूसरी रेखा पर (y=9) है। इसलिए उनका सामान्य बिंदु ( (4,9) ) है।
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समीकरण (x+2y=12) और (x+y=8) का ग्राफीय हल कौन-सा है?
Which is the graphical solution of (x+2y=12) and (x+y=8)?
#graphical solution
#intersection
#linear equations
A ( (4,4) )
B ( (6,2) )
C ( (2,6) )
D ( (8,0) )
Explanation opens after your attempt
Correct Answer
A. ( (4,4) )
Step 1
Concept
At ( (4,4) ), (4+2(4)=12) and (4+4=8). This is the intersection point of both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (4,4) ). At ( (4,4) ), (4+2(4)=12) and (4+4=8). This is the intersection point of both lines.
Step 3
Exam Tip
( (4,4) ) पर (4+2(4)=12) और (4+4=8)। यही दोनों रेखाओं का प्रतिच्छेद बिंदु है।
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रेखाएँ (x+3y=10) और (2x+3y=14) कहाँ मिलती हैं?
Where do the lines (x+3y=10) and (2x+3y=14) meet?
#graphical solution
#intersection
#linear equations
A ( (4,2) )
B ( (2,4) )
C ( (5,1) )
D ( (1,5) )
Explanation opens after your attempt
Correct Answer
A. ( (4,2) )
Step 1
Concept
At ( (4,2) ), (4+3(2)=10) and (2(4)+3(2)=14). Hence, this is the graphical solution.
Step 2
Why this answer is correct
The correct answer is A. ( (4,2) ). At ( (4,2) ), (4+3(2)=10) and (2(4)+3(2)=14). Hence, this is the graphical solution.
Step 3
Exam Tip
( (4,2) ) पर (4+3(2)=10) और (2(4)+3(2)=14)। इसलिए यह ग्राफीय हल है।
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रेखाएँ (x+2y=6) और (2x+y=6) किस बिंदु पर मिलती हैं?
At which point do the lines (x+2y=6) and (2x+y=6) meet?
#intersection
#graphical solution
#checking
A ( (1,4) )
B ( (4,1) )
C ( (2,2) )
D ( (3,3) )
Explanation opens after your attempt
Correct Answer
C. ( (2,2) )
Step 1
Concept
Substituting ( (2,2) ) gives (2+2(2)=6) and (2(2)+2=6). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is C. ( (2,2) ). Substituting ( (2,2) ) gives (2+2(2)=6) and (2(2)+2=6). This is the common point of both lines.
Step 3
Exam Tip
( (2,2) ) रखने पर (2+2(2)=6) और (2(2)+2=6)। यही दोनों रेखाओं का सामान्य बिंदु है।
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समीकरण (x+3y=13) और (x+y=7) का हल कौन-सा है?
Which is the solution of (x+3y=13) and (x+y=7)?
#graphical solution
#intersection
#checking
A ( (5,2) )
B ( (4,3) )
C ( (2,5) )
D ( (7,0) )
Explanation opens after your attempt
Correct Answer
A. ( (5,2) )
Step 1
Concept
Substituting ( (4,3) ) gives (4+3(3)=13) and (4+3=7). If both equations are satisfied, that is the intersection point.
Step 2
Why this answer is correct
The correct answer is A. ( (5,2) ). Substituting ( (4,3) ) gives (4+3(3)=13) and (4+3=7). If both equations are satisfied, that is the intersection point.
Step 3
Exam Tip
( (4,3) ) रखने पर (4+3(3)=13) और (4+3=7)। दोनों समीकरण संतुष्ट हों तो वही प्रतिच्छेद बिंदु है।
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रेखाएँ (x=9) और (y=3) किस बिंदु पर मिलेंगी?
At which point will the lines (x=9) and (y=3) meet?
#vertical horizontal lines
#intersection
#solution
A ( (3,9) )
B ( (9,3) )
C ( (9,0) )
D ( (0,3) )
Explanation opens after your attempt
Correct Answer
B. ( (9,3) )
Step 1
Concept
On the first line (x=9), and on the second line (y=3). Therefore, the common point is ( (9,3) ).
Step 2
Why this answer is correct
The correct answer is B. ( (9,3) ). On the first line (x=9), and on the second line (y=3). Therefore, the common point is ( (9,3) ).
Step 3
Exam Tip
पहली रेखा पर (x=9) और दूसरी पर (y=3) है। इसलिए सामान्य बिंदु ( (9,3) ) है।
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रेखा (x+y=2) और रेखा (x-y=2) कहाँ मिलेंगी?
Where will the lines (x+y=2) and (x-y=2) meet?
#linear equations
#intersection
#graphical solution
#easy
A ( (2,0) )
B ( (0,2) )
C ( (1,1) )
D ( (0,0) )
Explanation opens after your attempt
Correct Answer
A. ( (2,0) )
Step 1
Concept
At ( (2,0) ), (2+0=2) and (2-0=2). Hence, this is the intersection of both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (2,0) ). At ( (2,0) ), (2+0=2) and (2-0=2). Hence, this is the intersection of both lines.
Step 3
Exam Tip
( (2,0) ) पर (2+0=2) और (2-0=2)। अतः यही दोनों रेखाओं का प्रतिच्छेद है।
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यदि रेखा (x=4) और रेखा (y=5) मिलें, तो प्रतिच्छेद बिंदु क्या होगा?
If the line (x=4) and the line (y=5) meet, what is the intersection point?
#linear equations
#intersection
#vertical horizontal lines
#easy
A ( (4,5) )
B ( (5,4) )
C ( (4,0) )
D ( (0,5) )
Explanation opens after your attempt
Correct Answer
A. ( (4,5) )
Step 1
Concept
The line (x=4) has (x=4) for all its points and (y=5) has (y=5) for all its points. Their common point is ( (4,5) ).
Step 2
Why this answer is correct
The correct answer is A. ( (4,5) ). The line (x=4) has (x=4) for all its points and (y=5) has (y=5) for all its points. Their common point is ( (4,5) ).
Step 3
Exam Tip
रेखा (x=4) सभी बिंदुओं में (x=4) रखती है और (y=5) सभी बिंदुओं में (y=5) रखती है। दोनों का सामान्य बिंदु ( (4,5) ) है।
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समीकरण (x+y=4) और (x-y=2) का ग्राफीय हल कौन-सा है?
What is the graphical solution of (x+y=4) and (x-y=2)?
#linear equations
#graphical solution
#intersection
#easy
A ( (3,1) )
B ( (2,2) )
C ( (1,3) )
D ( (4,0) )
Explanation opens after your attempt
Correct Answer
A. ( (3,1) )
Step 1
Concept
The point ( (3,1) ) satisfies both (3+1=4) and (3-1=2). On the graph, this will be the intersection point.
Step 2
Why this answer is correct
The correct answer is A. ( (3,1) ). The point ( (3,1) ) satisfies both (3+1=4) and (3-1=2). On the graph, this will be the intersection point.
Step 3
Exam Tip
( (3,1) ) दोनों समीकरणों (3+1=4) और (3-1=2) को संतुष्ट करता है। ग्राफ पर यही दोनों रेखाओं का प्रतिच्छेद होगा।
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ग्राफीय विधि में दो रेखाओं के प्रतिच्छेद बिंदु का क्या अर्थ होता है?
In graphical method, what does the point of intersection of two lines represent?
#linear equations
#graphical method
#intersection
#solution
A दोनों समीकरणों का हल / Solution of both equations
B केवल पहले समीकरण का हल / Solution of only first equation
C केवल दूसरे समीकरण का हल / Solution of only second equation
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
A. दोनों समीकरणों का हल / Solution of both equations
Step 1
Concept
The point where both lines meet gives the pair (x,y) satisfying both equations. In exams, always treat the intersection point as the solution.
Step 2
Why this answer is correct
The correct answer is A. दोनों समीकरणों का हल / Solution of both equations. The point where both lines meet gives the pair (x,y) satisfying both equations. In exams, always treat the intersection point as the solution.
Step 3
Exam Tip
जहाँ दोनों रेखाएँ मिलती हैं वही युग्म (x,y) दोनों समीकरणों को संतुष्ट करता है। परीक्षा में प्रतिच्छेद बिंदु को हमेशा हल मानें।
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