The second equation must be (3) times the first, so (k=126). In coincident lines, the constant term also changes in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (126). The second equation must be (3) times the first, so (k=126). In coincident lines, the constant term also changes in the same ratio.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना होना चाहिए, इसलिए (k=126)। संपाती रेखाओं में स्थिर पद भी उसी अनुपात में बदलता है।
C. समाधान सेट वही रेखा (7x+8y=56) है/The solution set is the line (7x+8y=56)
Step 1
Concept
The second equation is (2) times the first, so both are the same line. The solution is all points on that line, not the whole plane.
Step 2
Why this answer is correct
The correct answer is C. समाधान सेट वही रेखा (7x+8y=56) है / The solution set is the line (7x+8y=56). The second equation is (2) times the first, so both are the same line. The solution is all points on that line, not the whole plane.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों एक ही रेखा हैं। समाधान उसी रेखा के सभी बिंदु हैं, पूरा तल नहीं।
The first equation is (5) times the second. Therefore the lines are coincident and give infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती / Coincident. The first equation is (5) times the second. Therefore the lines are coincident and give infinitely many solutions.
Step 3
Exam Tip
पहला समीकरण दूसरे का (5) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत समाधान देती हैं।
The second equation is (3) times the first, so (m=21). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (21). The second equation is (3) times the first, so (m=21). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है, इसलिए (m=21)। संपाती रेखा में (y) का गुणांक भी उसी अनुपात में बदलता है।
The first equation must be (4) times the second, so (a=20). In coincident lines, all terms change by the same multiplier.
Step 2
Why this answer is correct
The correct answer is C. (20). The first equation must be (4) times the second, so (a=20). In coincident lines, all terms change by the same multiplier.
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए, इसलिए (a=20)। संपाती रेखाओं में सभी पद समान गुणक से बदलते हैं।
If all three ratios are equal, both equations represent the same line. Hence the lines are coincident and give infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती / Coincident. If all three ratios are equal, both equations represent the same line. Hence the lines are coincident and give infinitely many solutions.
Step 3
Exam Tip
तीनों अनुपात बराबर हों तो दोनों समीकरण एक ही रेखा बताते हैं। इसलिए रेखाएं संपाती होती हैं और अनंत समाधान देती हैं।
The second equation is (2) times the first, so both lines are the same. All points on the same line are solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत समाधान / Infinitely many solutions. The second equation is (2) times the first, so both lines are the same. All points on the same line are solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों रेखाएं एक ही हैं। एक ही रेखा के सभी बिंदु समाधान होते हैं।
C. समाधान सेट वही रेखा (5x+6y=30) है/The solution set is the line (5x+6y=30)
Step 1
Concept
The second equation is (2) times the first, so both are the same line. The solution is all points on that line, not the whole plane.
Step 2
Why this answer is correct
The correct answer is C. समाधान सेट वही रेखा (5x+6y=30) है / The solution set is the line (5x+6y=30). The second equation is (2) times the first, so both are the same line. The solution is all points on that line, not the whole plane.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों एक ही रेखा हैं। समाधान उसी रेखा के सभी बिंदु हैं, पूरा तल नहीं।
The first equation is (3) times the second. Therefore the lines are coincident and give infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती / Coincident. The first equation is (3) times the second. Therefore the lines are coincident and give infinitely many solutions.
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत समाधान देती हैं।
The second equation is (2) times the first, so both are the same line. Only (1) distinct line will be visible on the graph.
Step 2
Why this answer is correct
The correct answer is B. (1). The second equation is (2) times the first, so both are the same line. Only (1) distinct line will be visible on the graph.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों एक ही रेखा हैं। ग्राफ पर केवल (1) अलग रेखा दिखाई देगी।
The second equation is (2) times the first, so (m=10). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (10). The second equation is (2) times the first, so (m=10). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए (m=10)। संपाती रेखा में (y) का गुणांक भी उसी अनुपात में बदलता है।
The first equation must be (3) times the second, so (a=12). In coincident lines, all terms change by the same multiplier.
Step 2
Why this answer is correct
The correct answer is C. (12). The first equation must be (3) times the second, so (a=12). In coincident lines, all terms change by the same multiplier.
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना होना चाहिए, इसलिए (a=12)। संपाती रेखाओं में सभी पद समान गुणक से बदलते हैं।
The second equation is (2) times the first, so both lines are the same. All points on the same line are solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत समाधान / Infinitely many solutions. The second equation is (2) times the first, so both lines are the same. All points on the same line are solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों रेखाएं एक ही हैं। एक ही रेखा के सभी बिंदु समाधान होते हैं।
C. समाधान सेट वही रेखा (2x+3y=5) है/The solution set is the line (2x+3y=5)
Step 1
Concept
The second equation is (2) times the first, so both are the same line. The solution is all points on that line, not the whole plane.
Step 2
Why this answer is correct
The correct answer is C. समाधान सेट वही रेखा (2x+3y=5) है / The solution set is the line (2x+3y=5). The second equation is (2) times the first, so both are the same line. The solution is all points on that line, not the whole plane.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों एक ही रेखा हैं। समाधान उसी रेखा के सभी बिंदु हैं, पूरा तल नहीं।
The first equation is (3) times the second. Therefore the lines are coincident and give infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती / Coincident. The first equation is (3) times the second. Therefore the lines are coincident and give infinitely many solutions.
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत समाधान देती हैं।
Both equations are the same line, so only one distinct line will be visible on the graph. This is the case of infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. (1). Both equations are the same line, so only one distinct line will be visible on the graph. This is the case of infinitely many solutions.
Step 3
Exam Tip
दोनों समीकरण एक ही रेखा हैं, इसलिए ग्राफ पर एक ही अलग रेखा दिखेगी। यह अनंत समाधान की स्थिति है।
C. उस समान रेखा का हर बिंदु समाधान है/Every point on that same line is a solution
Step 1
Concept
Coincident lines represent the same line. Therefore every point on that line satisfies both equations.
Step 2
Why this answer is correct
The correct answer is C. उस समान रेखा का हर बिंदु समाधान है / Every point on that same line is a solution. Coincident lines represent the same line. Therefore every point on that line satisfies both equations.
Step 3
Exam Tip
संपाती रेखाओं में दोनों समीकरण एक ही रेखा को दर्शाते हैं। इसलिए उस रेखा का हर बिंदु दोनों समीकरणों को संतुष्ट करता है।
