What is found by comparing the first two ratios in (4x+y=9) and (7x+2y=13)?
Answer and explanation
Correct answer: (4/7 ≠ 1/2), so one unique solution
For the equations 4x+y=9 and 7x+2y=13, compare the ratios of the coefficients of x and y. We obtain a₁/a₂=4/7 and b₁/b₂=1/2. Since 4/7 is not equal to 1/2, the two coefficient ratios are unequal. This is the condition for two non-parallel lines, so their graphs intersect at exactly one point and the pair has one unique solution. The constant-term ratio 9/13 need not be compared to establish this conclusion once the first two ratios differ. Option A contains a false equality, while C and D would describe coincident lines. Therefore B is correct.
Frequently asked questions
What is the correct answer to this question?
(4/7 ≠ 1/2), so one unique solution
Why is this the correct answer?
For the equations 4x+y=9 and 7x+2y=13, compare the ratios of the coefficients of x and y. We obtain a₁/a₂=4/7 and b₁/b₂=1/2. Since 4/7 is not equal to 1/2, the two coefficient ratios are unequal. This is the condition for two non-parallel lines, so their graphs intersect at exactly one point and the pair has one unique solution. The constant-term ratio 9/13 need not be compared to establish this conclusion once the first two ratios differ. Option A contains a false equality, while C and D would describe coincident lines. Therefore B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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