What is found by comparing the ratios of (a) and (b) in (11x+6y=35) and (5x+3y=17)?
Answer and explanation
Correct answer: (11/5 \ne 6/3) so one unique solution
The coefficient-ratio test determines how two linear equations are related. If the ratios of the x and y coefficients are different, the lines have different slopes. Different slopes guarantee one intersection point, which means the pair is consistent and independent and has a unique solution. The constant terms do not change this conclusion once the first two ratios are unequal.
For these equations, \\(11/5=2.2\\), but \\(6/3=2\\). Hence \\(11/5\\ne6/3\\). The lines therefore have different slopes and intersect at exactly one point. They cannot be coincident, because coincident lines would have equal ratios for all corresponding coefficients. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
(11/5 \ne 6/3) so one unique solution
Why is this the correct answer?
The coefficient-ratio test determines how two linear equations are related. If the ratios of the x and y coefficients are different, the lines have different slopes. Different slopes guarantee one intersection point, which means the pair is consistent and independent and has a unique solution. The constant terms do not change this conclusion once the first two ratios are unequal.
For these equations, \\(11/5=2.2\\), but \\(6/3=2\\). Hence \\(11/5\\ne6/3\\). The lines therefore have different slopes and intersect at exactly one point. They cannot be coincident, because coincident lines would have equal ratios for all corresponding coefficients. Thus option C 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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