What is found by comparing the ratios of (a) and (b) in the equations (11x+6y=35) and (5x+3y=17)?
Answer and explanation
Correct answer: (11/5 \ne 6/3) so one unique solution
The equations in this item are the same as in the preceding comparison, and the relevant rule is unchanged. When the ratio of the x coefficients differs from the ratio of the y coefficients, the two lines have different slopes. Two lines with different slopes intersect once, so the pair has exactly one solution. Equality of both variable ratios would be needed for parallel or coincident-line tests.
Calculate the ratios: \\(11/5=2.2\\) and \\(6/3=2\\). Since these values are unequal, \\(11/5\\ne6/3\\). The lines cannot be parallel with the same slope, and they cannot be the same line. They meet at one point, so the system has a unique solution. Therefore option C agrees with the mathematics.
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 equations in this item are the same as in the preceding comparison, and the relevant rule is unchanged. When the ratio of the x coefficients differs from the ratio of the y coefficients, the two lines have different slopes. Two lines with different slopes intersect once, so the pair has exactly one solution. Equality of both variable ratios would be needed for parallel or coincident-line tests.
Calculate the ratios: \\(11/5=2.2\\) and \\(6/3=2\\). Since these values are unequal, \\(11/5\\ne6/3\\). The lines cannot be parallel with the same slope, and they cannot be the same line. They meet at one point, so the system has a unique solution. Therefore option C agrees with the mathematics.
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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