What is found by comparing the ratios of (a) and (b) in the equations (17x+10y=61) and (8x+5y=29)?
Answer and explanation
Correct answer: (17/8 \ne 10/5) so one unique solution
The relationship between two linear equations can be classified by comparing corresponding coefficient ratios. Unequal ratios for the x and y coefficients show that the lines have unequal slopes. Such lines cannot be parallel or identical; they intersect at one point and therefore produce one unique solution.
For this pair, \\(17/8=2.125\\), whereas \\(10/5=2\\). Thus \\(17/8\\ne10/5\\). Because the first two ratios are unequal, the equations represent two lines with different directions. They meet at exactly one point, regardless of the constant-term ratio. Therefore the correct conclusion is one unique solution, given in option C.
Frequently asked questions
What is the correct answer to this question?
(17/8 \ne 10/5) so one unique solution
Why is this the correct answer?
The relationship between two linear equations can be classified by comparing corresponding coefficient ratios. Unequal ratios for the x and y coefficients show that the lines have unequal slopes. Such lines cannot be parallel or identical; they intersect at one point and therefore produce one unique solution.
For this pair, \\(17/8=2.125\\), whereas \\(10/5=2\\). Thus \\(17/8\\ne10/5\\). Because the first two ratios are unequal, the equations represent two lines with different directions. They meet at exactly one point, regardless of the constant-term ratio. Therefore the correct conclusion is one unique solution, given in option C.
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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