दो राशियों के लिए (5x+5y=140) और (6x-6y=24) हैं। ग्राफीय विधि से समाधान कौन सा होगा?
For two quantities, (5x+5y=140) and (6x-6y=24). What will be the solution by graphical method?
#graphical method
#simultaneous equations
#intersection
#numerical
A ((16,12))
B ((12,16))
C ((18,10))
D ((14,14))
Explanation opens after your attempt
Correct Answer
A. ((16,12))
Step 1
Concept
Simplifying gives (x+y=28) and (x-y=4). Their intersection is ((16,12)).
Step 2
Why this answer is correct
The correct answer is A. ((16,12)). Simplifying gives (x+y=28) and (x-y=4). Their intersection is ((16,12)).
Step 3
Exam Tip
सरल करने पर (x+y=28) और (x-y=4) मिलते हैं। इनका प्रतिच्छेद ((16,12)) है।
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यदि (5x-y=19) और (x+y=5) का ग्राफीय समाधान ((p,q)) है, तो (p-q) क्या होगा?
If the graphical solution of (5x-y=19) and (x+y=5) is ((p,q)), what is (p-q)?
#graphical solution
#smart solving
#intersection
#exam trick
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Solving gives (p=4) and (q=1). Therefore (p-q=3), which comes from the intersection point.
Step 2
Why this answer is correct
The correct answer is C. (3). Solving gives (p=4) and (q=1). Therefore (p-q=3), which comes from the intersection point.
Step 3
Exam Tip
हल करने पर (p=4) और (q=1) मिलता है। इसलिए (p-q=3), और यही प्रतिच्छेद से निकला मान है।
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यदि दो रेखाओं का एकमात्र प्रतिच्छेद ((r,s)) है और (4r+s=29), (r-s=1), तो (r+s) क्या है?
If the only intersection of two lines is ((r,s)) and (4r+s=29), (r-s=1), what is (r+s)?
#graphical method
#intersection
#coordinate sum
#expert reasoning
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
Putting (s=r-1) gives (4r+r-1=29), so (r=6) and (s=5). Therefore (r+s=11).
Step 2
Why this answer is correct
The correct answer is C. (11). Putting (s=r-1) gives (4r+r-1=29), so (r=6) and (s=5). Therefore (r+s=11).
Step 3
Exam Tip
(s=r-1) रखने पर (4r+r-1=29), इसलिए (r=6) और (s=5)। अतः (r+s=11)।
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एक दुकान में दो वस्तुओं की कुल कीमत (154) है और पहली वस्तु दूसरी से (22) महंगी है। ग्राफीय समाधान कौन सा है?
In a shop, the total cost of two items is (154), and the first item is (22) costlier than the second. What is the graphical solution?
#graphical method
#word problem
#application
#intersection
A ((88,66))
B ((66,88))
C ((87,67))
D ((90,64))
Explanation opens after your attempt
Correct Answer
A. ((88,66))
Step 1
Concept
The equations are (x+y=154) and (x-y=22). Solving gives (x=88), (y=66), which is the graph intersection.
Step 2
Why this answer is correct
The correct answer is A. ((88,66)). The equations are (x+y=154) and (x-y=22). Solving gives (x=88), (y=66), which is the graph intersection.
Step 3
Exam Tip
समीकरण (x+y=154) और (x-y=22) हैं। इन्हें हल करने पर (x=88), (y=66), जो ग्राफ का प्रतिच्छेद है।
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एक ग्राफ में दो रेखाएं ((-4,1)) पर प्रतिच्छेद करती हैं। कौन सा समीकरण युग्म सही है?
Two lines intersect at ((-4,1)) on a graph. Which pair of equations is correct?
#graphical method
#intersection
#negative coordinates
#verification
A (x+y=-3), (2x-y=-9)
B (x+y=3), (2x-y=-9)
C (x-y=-3), (2x+y=-9)
D (x+y=-3), (2x-y=9)
Explanation opens after your attempt
Correct Answer
A. (x+y=-3), (2x-y=-9)
Step 1
Concept
Substituting ((-4,1)) makes (x+y=-3) and (2x-y=-9) both true. Substituting the intersection point in both equations is the fastest check.
Step 2
Why this answer is correct
The correct answer is A. (x+y=-3), (2x-y=-9). Substituting ((-4,1)) makes (x+y=-3) and (2x-y=-9) both true. Substituting the intersection point in both equations is the fastest check.
Step 3
Exam Tip
((-4,1)) रखने पर (x+y=-3) और (2x-y=-9) दोनों सही हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में रखना सबसे तेज जांच है।
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ग्राफ में (6x+y=38) और (3x-2y=-1) का समाधान कौन सा है?
What is the solution of (6x+y=38) and (3x-2y=-1) on the graph?
#graphical solution
#substitution
#intersection
#numerical
A ((5,8))
B ((6,2))
C ((4,14))
D ((3,20))
Explanation opens after your attempt
Correct Answer
A. ((5,8))
Step 1
Concept
From the first equation, (y=38-6x). Substituting gives (3x-2(38-6x)=-1), so (x=5), (y=8). This is the graph intersection.
Step 2
Why this answer is correct
The correct answer is A. ((5,8)). From the first equation, (y=38-6x). Substituting gives (3x-2(38-6x)=-1), so (x=5), (y=8). This is the graph intersection.
Step 3
Exam Tip
पहले से (y=38-6x), दूसरे में रखने पर (3x-2(38-6x)=-1), इसलिए (x=5), (y=8)। यही ग्राफ का प्रतिच्छेद है।
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दो राशियों के लिए (3x+3y=99) और (4x-4y=28) हैं। ग्राफीय समाधान कौन सा है?
For two quantities, (3x+3y=99) and (4x-4y=28). What is the graphical solution?
#graphical method
#word problem
#simplification
#intersection
A ((20,13))
B ((13,20))
C ((21,12))
D ((19,14))
Explanation opens after your attempt
Correct Answer
A. ((20,13))
Step 1
Concept
Simplifying gives (x+y=33) and (x-y=7). Their intersection is ((20,13)).
Step 2
Why this answer is correct
The correct answer is A. ((20,13)). Simplifying gives (x+y=33) and (x-y=7). Their intersection is ((20,13)).
Step 3
Exam Tip
सरल करने पर (x+y=33) और (x-y=7) मिलते हैं। इनका प्रतिच्छेद ((20,13)) है।
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एक कक्षा में दो समूहों के विद्यार्थियों की कुल संख्या (74) है और पहले समूह में दूसरे से (16) विद्यार्थी अधिक हैं। ग्राफीय समाधान क्या होगा?
In a class, the total number of students in two groups is (74), and the first group has (16) more students than the second. What will be the graphical solution?
#graphical method
#word problem
#intersection
#application
A ((45,29))
B ((29,45))
C ((44,30))
D ((46,28))
Explanation opens after your attempt
Correct Answer
A. ((45,29))
Step 1
Concept
The equations are (x+y=74) and (x-y=16), giving (x=45), (y=29). In word problems, first define the variables clearly.
Step 2
Why this answer is correct
The correct answer is A. ((45,29)). The equations are (x+y=74) and (x-y=16), giving (x=45), (y=29). In word problems, first define the variables clearly.
Step 3
Exam Tip
समीकरण (x+y=74) और (x-y=16) हैं, जिनसे (x=45), (y=29)। शब्द-प्रश्न में पहले चर स्पष्ट तय करें।
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एक ग्राफ में दो रेखाएं (A(-1,6)) पर मिलती हैं। कौन सा युग्म इसे सत्यापित करता है?
Two lines meet at (A(-1,6)) on a graph. Which pair verifies this?
#graphical method
#point verification
#intersection
#ordered pair
A (2x+y=4), (x-y=-7)
B (2x+y=5), (x-y=-7)
C (2x-y=4), (x-y=-7)
D (2x+y=4), (x+y=-7)
Explanation opens after your attempt
Correct Answer
A. (2x+y=4), (x-y=-7)
Step 1
Concept
Substituting ((-1,6)) makes (2x+y=4) and (x-y=-7) both true. The intersection point must lie on both lines.
Step 2
Why this answer is correct
The correct answer is A. (2x+y=4), (x-y=-7). Substituting ((-1,6)) makes (2x+y=4) and (x-y=-7) both true. The intersection point must lie on both lines.
Step 3
Exam Tip
((-1,6)) रखने पर (2x+y=4) और (x-y=-7) दोनों सही हैं। प्रतिच्छेद बिंदु दोनों रेखाओं पर होना चाहिए।
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रेखाएं (3x+2y=25) और (x-3y=-11) ग्राफ पर किस बिंदु पर मिलती हैं?
At which point do (3x+2y=25) and (x-3y=-11) meet on the graph?
#graphical solution
#intersection
#substitution
#numerical
A ((5,5))
B ((7,2))
C ((3,8))
D (\(6,\frac{7}{2}\))
Explanation opens after your attempt
Correct Answer
A. ((5,5))
Step 1
Concept
From the second equation, (x=3y-11). Substituting gives (9y-33+2y=25), so (y=5). Then (x=5), so the intersection is ((5,5)).
Step 2
Why this answer is correct
The correct answer is A. ((5,5)). From the second equation, (x=3y-11). Substituting gives (9y-33+2y=25), so (y=5). Then (x=5), so the intersection is ((5,5)).
Step 3
Exam Tip
दूसरे से (x=3y-11), पहले में रखने पर (9y-33+2y=25), इसलिए (y=5)। फिर (x=5), अतः प्रतिच्छेद ((5,5)) है।
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ग्राफ पर (4x-y=13) और (x+2y=14) का समाधान कौन सा है?
What is the solution of (4x-y=13) and (x+2y=14) on the graph?
#graphical solution
#intersection
#substitution
#numerical
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
From the first equation, (y=4x-13). Substituting gives (x+2(4x-13)=14), so (x=4) and (y=3). The intersection point is the graphical solution.
Step 2
Why this answer is correct
The correct answer is A. ((4,3)). From the first equation, (y=4x-13). Substituting gives (x+2(4x-13)=14), so (x=4) and (y=3). The intersection point is the graphical solution.
Step 3
Exam Tip
पहले से (y=4x-13), दूसरे में रखने पर (x+2(4x-13)=14), इसलिए (x=4) और (y=3)। प्रतिच्छेद बिंदु ही ग्राफीय हल है।
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यदि (y=-4) और (5x+2y=17) को ग्राफ किया जाए, तो प्रतिच्छेद बिंदु क्या होगा?
If (y=-4) and (5x+2y=17) are graphed, what will be the intersection point?
#graphical method
#horizontal line
#intersection
#numerical
A ((5,-4))
B ((-4,5))
C ((3,-4))
D ((4,-5))
Explanation opens after your attempt
Correct Answer
A. ((5,-4))
Step 1
Concept
Putting (y=-4) gives (5x-8=17), so (x=5). In a horizontal line, the (y)-coordinate remains fixed.
Step 2
Why this answer is correct
The correct answer is A. ((5,-4)). Putting (y=-4) gives (5x-8=17), so (x=5). In a horizontal line, the (y)-coordinate remains fixed.
Step 3
Exam Tip
(y=-4) रखने पर (5x-8=17), इसलिए (x=5)। क्षैतिज रेखा में (y)-निर्देशांक स्थिर रहता है।
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ग्राफ पर (x=-5) और (3x+2y=9) का समाधान कौन सा है?
What is the graphical solution of (x=-5) and (3x+2y=9)?
#graphical method
#vertical line
#intersection
#numerical
A ((-5,12))
B ((12,-5))
C ((-5,9))
D ((5,12))
Explanation opens after your attempt
Correct Answer
A. ((-5,12))
Step 1
Concept
Putting (x=-5) gives (-15+2y=9), so (y=12). With a vertical line, the (x)-coordinate is already fixed.
Step 2
Why this answer is correct
The correct answer is A. ((-5,12)). Putting (x=-5) gives (-15+2y=9), so (y=12). With a vertical line, the (x)-coordinate is already fixed.
Step 3
Exam Tip
(x=-5) रखने पर (-15+2y=9), इसलिए (y=12)। ऊर्ध्वाधर रेखा के साथ (x)-निर्देशांक पहले से तय रहता है।
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यदि ग्राफ में दो रेखाओं का प्रतिच्छेद (\left\(\frac{5}{2},-\frac{3}{2}\right\)) है, तो कौन सा युग्म सही हो सकता है?
If the intersection of two lines on a graph is (\left\(\frac{5}{2},-\frac{3}{2}\right\)), which pair can be correct?
#graphical method
#point verification
#fractional coordinates
#intersection
A \(2x+y=\frac{7}{2}\), \(x-2y=\frac{11}{2}\)
B \(2x-y=\frac{7}{2}\), \(x-2y=\frac{11}{2}\)
C \(2x+y=\frac{11}{2}\), \(x-2y=\frac{7}{2}\)
D \(2x+y=\frac{7}{2}\), \(x+2y=\frac{11}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2x+y=\frac{7}{2}\), \(x-2y=\frac{11}{2}\)
Step 1
Concept
Substituting (\left\(\frac{5}{2},-\frac{3}{2}\right\)) makes both \(2x+y=\frac{7}{2}\) and \(x-2y=\frac{11}{2}\) true. Check the intersection point in both equations.
Step 2
Why this answer is correct
The correct answer is A. \(2x+y=\frac{7}{2}\), \(x-2y=\frac{11}{2}\). Substituting (\left\(\frac{5}{2},-\frac{3}{2}\right\)) makes both \(2x+y=\frac{7}{2}\) and \(x-2y=\frac{11}{2}\) true. Check the intersection point in both equations.
Step 3
Exam Tip
(\left\(\frac{5}{2},-\frac{3}{2}\right\)) रखने पर \(2x+y=\frac{7}{2}\) और \(x-2y=\frac{11}{2}\) दोनों सत्य हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में जांचें।
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रेखाएं (5x+2y=24) और (x-y=3) ग्राफ पर किस बिंदु पर मिलेंगी?
At which point will the lines (5x+2y=24) and (x-y=3) meet on the graph?
#graphical solution
#intersection
#substitution
#numerical
A ((6,3))
B ((4,6))
C ((3,6))
D ((5,4))
Explanation opens after your attempt
Correct Answer
A. ((6,3))
Step 1
Concept
From (x-y=3), (y=x-3); substituting gives (7x-6=24) and (x=6). Thus (y=3), so the intersection is ((6,3)).
Step 2
Why this answer is correct
The correct answer is A. ((6,3)). From (x-y=3), (y=x-3); substituting gives (7x-6=24) and (x=6). Thus (y=3), so the intersection is ((6,3)).
Step 3
Exam Tip
(x-y=3) से (y=x-3), रखने पर (7x-6=24) और (x=6)। इसलिए (y=3), अतः प्रतिच्छेद ((6,3)) है।
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दो संख्याओं के लिए (2x+y=37) और (x+2y=32) हैं। ग्राफीय विधि से समाधान कौन सा होगा?
For two numbers, (2x+y=37) and (x+2y=32). What will be the solution by graphical method?
#graphical method
#simultaneous equations
#intersection
#numerical
A ((14,9))
B ((9,14))
C ((15,7))
D ((13,11))
Explanation opens after your attempt
Correct Answer
A. ((14,9))
Step 1
Concept
Solving both equations gives (x=14) and (y=9). On the graph, the intersection of the two lines will be ((14,9)).
Step 2
Why this answer is correct
The correct answer is A. ((14,9)). Solving both equations gives (x=14) and (y=9). On the graph, the intersection of the two lines will be ((14,9)).
Step 3
Exam Tip
दोनों समीकरणों को हल करने पर (x=14) और (y=9) मिलता है। ग्राफ में दोनों रेखाओं का प्रतिच्छेद ((14,9)) होगा।
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यदि (4x-y=11) और (x+y=4) का ग्राफीय समाधान ((p,q)) है, तो (p-q) क्या होगा?
If the graphical solution of (4x-y=11) and (x+y=4) is ((p,q)), what is (p-q)?
#graphical solution
#smart solving
#intersection
#exam trick
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Solving gives (p=3) and (q=1). Therefore (p-q=2), which comes from the intersection point.
Step 2
Why this answer is correct
The correct answer is B. (2). Solving gives (p=3) and (q=1). Therefore (p-q=2), which comes from the intersection point.
Step 3
Exam Tip
हल करने पर (p=3) और (q=1) मिलता है। इसलिए (p-q=2), और यही प्रतिच्छेद से निकला मान है।
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यदि दो रेखाओं का एकमात्र प्रतिच्छेद ((r,s)) है और (3r+s=19), (r-s=1), तो (r+s) क्या है?
If the only intersection of two lines is ((r,s)) and (3r+s=19), (r-s=1), what is (r+s)?
#graphical method
#intersection
#coordinate sum
#expert reasoning
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Putting (s=r-1) gives (3r+r-1=19), so (r=5) and (s=4). Therefore (r+s=9).
Step 2
Why this answer is correct
The correct answer is B. (9). Putting (s=r-1) gives (3r+r-1=19), so (r=5) and (s=4). Therefore (r+s=9).
Step 3
Exam Tip
(s=r-1) रखने पर (3r+r-1=19), इसलिए (r=5) और (s=4)। अतः (r+s=9)।
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एक दुकान में दो वस्तुओं की कुल कीमत (126) है और पहली वस्तु दूसरी से (18) महंगी है। ग्राफीय समाधान कौन सा है?
In a shop, the total cost of two items is (126), and the first item is (18) costlier than the second. What is the graphical solution?
#graphical method
#word problem
#application
#intersection
A ((72,54))
B ((54,72))
C ((70,56))
D ((74,52))
Explanation opens after your attempt
Correct Answer
A. ((72,54))
Step 1
Concept
The equations are (x+y=126) and (x-y=18). Solving gives (x=72), (y=54), which is the graph intersection.
Step 2
Why this answer is correct
The correct answer is A. ((72,54)). The equations are (x+y=126) and (x-y=18). Solving gives (x=72), (y=54), which is the graph intersection.
Step 3
Exam Tip
समीकरण (x+y=126) और (x-y=18) हैं। इन्हें हल करने पर (x=72), (y=54), जो ग्राफ का प्रतिच्छेद है।
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एक ग्राफ में दो रेखाएं ((-2,-3)) पर प्रतिच्छेद करती हैं। कौन सा समीकरण युग्म सही है?
Two lines intersect at ((-2,-3)) on a graph. Which pair of equations is correct?
#graphical method
#intersection
#negative coordinates
#verification
A (x+y=-5), (2x-y=-1)
B (x+y=5), (2x-y=-1)
C (x-y=-5), (2x+y=-1)
D (x+y=-5), (2x-y=1)
Explanation opens after your attempt
Correct Answer
A. (x+y=-5), (2x-y=-1)
Step 1
Concept
Substituting ((-2,-3)) makes (x+y=-5) and (2x-y=-1) both true. Substituting the intersection point in both equations is the fastest check.
Step 2
Why this answer is correct
The correct answer is A. (x+y=-5), (2x-y=-1). Substituting ((-2,-3)) makes (x+y=-5) and (2x-y=-1) both true. Substituting the intersection point in both equations is the fastest check.
Step 3
Exam Tip
((-2,-3)) रखने पर (x+y=-5) और (2x-y=-1) दोनों सही हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में रखना सबसे तेज जांच है।
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ग्राफ में (5x+y=27) और (2x-3y=-6) का समाधान कौन सा है?
What is the solution of (5x+y=27) and (2x-3y=-6) on the graph?
#graphical solution
#substitution
#intersection
#numerical
A ((5,2))
B ((6,-3))
C ((4,7))
D ((3,12))
Explanation opens after your attempt
Correct Answer
A. ((5,2))
Step 1
Concept
From the first equation, (y=27-5x). Substituting gives (2x-3(27-5x)=-6), so (x=5), (y=2). This is the graph intersection.
Step 2
Why this answer is correct
The correct answer is A. ((5,2)). From the first equation, (y=27-5x). Substituting gives (2x-3(27-5x)=-6), so (x=5), (y=2). This is the graph intersection.
Step 3
Exam Tip
पहले से (y=27-5x), दूसरे में रखने पर (2x-3(27-5x)=-6), इसलिए (x=5), (y=2)। यही ग्राफ का प्रतिच्छेद है।
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दो राशियों के लिए (2x+2y=72) और (3x-3y=18) हैं। ग्राफीय समाधान कौन सा है?
For two quantities, (2x+2y=72) and (3x-3y=18). What is the graphical solution?
#graphical method
#word problem
#simplification
#intersection
A ((21,15))
B ((15,21))
C ((20,16))
D ((22,14))
Explanation opens after your attempt
Correct Answer
A. ((21,15))
Step 1
Concept
Simplifying gives (x+y=36) and (x-y=6). Their intersection is ((21,15)).
Step 2
Why this answer is correct
The correct answer is A. ((21,15)). Simplifying gives (x+y=36) and (x-y=6). Their intersection is ((21,15)).
Step 3
Exam Tip
सरल करने पर (x+y=36) और (x-y=6) मिलते हैं। इनका प्रतिच्छेद ((21,15)) है।
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एक पुस्तकालय में दो प्रकार की पुस्तकों की कुल संख्या (58) है और पहले प्रकार की संख्या दूसरे से (12) अधिक है। ग्राफीय समाधान क्या होगा?
A library has (58) books of two types, and the first type is (12) more than the second. What will be the graphical solution?
#graphical method
#word problem
#intersection
#application
A ((35,23))
B ((23,35))
C ((34,24))
D ((36,22))
Explanation opens after your attempt
Correct Answer
A. ((35,23))
Step 1
Concept
The equations are (x+y=58) and (x-y=12), giving (x=35), (y=23). In word problems, first define the variables clearly.
Step 2
Why this answer is correct
The correct answer is A. ((35,23)). The equations are (x+y=58) and (x-y=12), giving (x=35), (y=23). In word problems, first define the variables clearly.
Step 3
Exam Tip
समीकरण (x+y=58) और (x-y=12) हैं, जिनसे (x=35), (y=23)। शब्द-प्रश्न में पहले चर स्पष्ट तय करें।
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एक ग्राफ में दो रेखाएं (A(2,-5)) पर मिलती हैं। कौन सा युग्म इसे सत्यापित करता है?
Two lines meet at (A(2,-5)) on a graph. Which pair verifies this?
#graphical method
#point verification
#intersection
#ordered pair
A (3x+y=1), (x-y=7)
B (3x+y=2), (x-y=7)
C (3x-y=1), (x-y=7)
D (3x+y=1), (x+y=7)
Explanation opens after your attempt
Correct Answer
A. (3x+y=1), (x-y=7)
Step 1
Concept
Substituting ((2,-5)) makes (3x+y=1) and (x-y=7) both true. The intersection point must lie on both lines.
Step 2
Why this answer is correct
The correct answer is A. (3x+y=1), (x-y=7). Substituting ((2,-5)) makes (3x+y=1) and (x-y=7) both true. The intersection point must lie on both lines.
Step 3
Exam Tip
((2,-5)) रखने पर (3x+y=1) और (x-y=7) दोनों सही हैं। प्रतिच्छेद बिंदु दोनों रेखाओं पर होना चाहिए।
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रेखाएं (2x+y=16) और (x-2y=-8) ग्राफ पर किस बिंदु पर मिलती हैं?
At which point do (2x+y=16) and (x-2y=-8) meet on the graph?
#graphical solution
#intersection
#substitution
#numerical
A ((4,8))
B ((8,4))
C ((6,4))
D ((2,12))
Explanation opens after your attempt
Correct Answer
A. ((4,8))
Step 1
Concept
From the first equation, (y=16-2x). Substituting gives (x-2(16-2x)=-8), so (x=4). Then (y=8).
Step 2
Why this answer is correct
The correct answer is A. ((4,8)). From the first equation, (y=16-2x). Substituting gives (x-2(16-2x)=-8), so (x=4). Then (y=8).
Step 3
Exam Tip
पहले से (y=16-2x), दूसरे में रखने पर (x-2(16-2x)=-8), इसलिए (x=4)। फिर (y=8)।
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ग्राफ पर (3x-y=10) और (2x+y=15) का समाधान कौन सा है?
What is the solution of (3x-y=10) and (2x+y=15) on the graph?
#graphical solution
#intersection
#elimination
#numerical
A ((5,5))
B ((4,3))
C ((6,2))
D ((3,4))
Explanation opens after your attempt
Correct Answer
A. ((5,5))
Step 1
Concept
Adding the two equations gives (5x=25), so (x=5) and (y=5). The intersection point is the graphical solution.
Step 2
Why this answer is correct
The correct answer is A. ((5,5)). Adding the two equations gives (5x=25), so (x=5) and (y=5). The intersection point is the graphical solution.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (5x=25), इसलिए (x=5) और (y=5)। प्रतिच्छेद बिंदु ही ग्राफीय हल है।
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यदि (y=-2) और (4x+3y=10) को ग्राफ किया जाए, तो प्रतिच्छेद बिंदु क्या होगा?
If (y=-2) and (4x+3y=10) are graphed, what will be the intersection point?
#graphical method
#horizontal line
#intersection
#numerical
A ((4,-2))
B ((-2,4))
C ((2,-4))
D ((5,-2))
Explanation opens after your attempt
Correct Answer
A. ((4,-2))
Step 1
Concept
Putting (y=-2) gives (4x-6=10), so (x=4). In a horizontal line, the (y)-coordinate remains fixed.
Step 2
Why this answer is correct
The correct answer is A. ((4,-2)). Putting (y=-2) gives (4x-6=10), so (x=4). In a horizontal line, the (y)-coordinate remains fixed.
Step 3
Exam Tip
(y=-2) रखने पर (4x-6=10), इसलिए (x=4)। क्षैतिज रेखा में (y)-निर्देशांक स्थिर रहता है।
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ग्राफ पर (x=-4) और (2x+3y=7) का समाधान कौन सा है?
What is the graphical solution of (x=-4) and (2x+3y=7)?
#graphical method
#vertical line
#intersection
#numerical
A ((-4,5))
B ((5,-4))
C ((-4,3))
D ((4,5))
Explanation opens after your attempt
Correct Answer
A. ((-4,5))
Step 1
Concept
Putting (x=-4) gives (-8+3y=7), so (y=5). With a vertical line, the (x)-coordinate is already fixed.
Step 2
Why this answer is correct
The correct answer is A. ((-4,5)). Putting (x=-4) gives (-8+3y=7), so (y=5). With a vertical line, the (x)-coordinate is already fixed.
Step 3
Exam Tip
(x=-4) रखने पर (-8+3y=7), इसलिए (y=5)। ऊर्ध्वाधर रेखा के साथ (x)-निर्देशांक पहले से तय रहता है।
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यदि ग्राफ में दो रेखाओं का प्रतिच्छेद (\left\(-\frac{3}{2},4\right\)) है, तो कौन सा युग्म सही हो सकता है?
If the intersection of two lines on a graph is (\left\(-\frac{3}{2},4\right\)), which pair can be correct?
#graphical method
#point verification
#fractional coordinates
#intersection
A (2x+y=1), \(x+2y=\frac{13}{2}\)
B (2x+y=-1), \(x+2y=\frac{13}{2}\)
C (2x-y=1), \(x+2y=\frac{13}{2}\)
D (2x+y=1), \(x-2y=\frac{13}{2}\)
Explanation opens after your attempt
Correct Answer
A. (2x+y=1), \(x+2y=\frac{13}{2}\)
Step 1
Concept
Substituting (\left\(-\frac{3}{2},4\right\)) makes both (2x+y=1) and \(x+2y=\frac{13}{2}\) true. The intersection point should be checked in both equations.
Step 2
Why this answer is correct
The correct answer is A. (2x+y=1), \(x+2y=\frac{13}{2}\). Substituting (\left\(-\frac{3}{2},4\right\)) makes both (2x+y=1) and \(x+2y=\frac{13}{2}\) true. The intersection point should be checked in both equations.
Step 3
Exam Tip
(\left\(-\frac{3}{2},4\right\)) रखने पर (2x+y=1) और \(x+2y=\frac{13}{2}\) दोनों सत्य हैं। प्रतिच्छेद बिंदु को दोनों समीकरणों में जांचना चाहिए।
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रेखाएं (3x+2y=18) और (x-y=1) ग्राफ पर किस बिंदु पर मिलेंगी?
At which point will the lines (3x+2y=18) and (x-y=1) meet on the graph?
#graphical solution
#intersection
#substitution
#numerical
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
From (x-y=1), (y=x-1); substituting gives (3x+2x-2=18) and (x=4). Thus (y=3), so the intersection is ((4,3)).
Step 2
Why this answer is correct
The correct answer is A. ((4,3)). From (x-y=1), (y=x-1); substituting gives (3x+2x-2=18) and (x=4). Thus (y=3), so the intersection is ((4,3)).
Step 3
Exam Tip
(x-y=1) से (y=x-1), रखने पर (3x+2x-2=18) और (x=4)। इसलिए (y=3), अतः प्रतिच्छेद ((4,3)) है।
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