What type of pair is (10x+15y=25) and (2x+3y=8)?
Answer and explanation
Correct answer: Inconsistent
For the two equations, \(\frac{a_1}{a_2}=\frac{10}{2}=5\) and \(\frac{b_1}{b_2}=\frac{15}{3}=5\), but \(\frac{c_1}{c_2}=\frac{25}{8}\). Since \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the two lines are distinct and parallel. Hence, the pair is inconsistent and has no solution. Option B would be correct only if all three ratios were equal. Exam tip: Compare all three coefficient ratios in such questions.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
For the two equations, \(\frac{a_1}{a_2}=\frac{10}{2}=5\) and \(\frac{b_1}{b_2}=\frac{15}{3}=5\), but \(\frac{c_1}{c_2}=\frac{25}{8}\). Since \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the two lines are distinct and parallel. Hence, the pair is inconsistent and has no solution. Option B would be correct only if all three ratios were equal. Exam tip: Compare all three coefficient ratios in such questions.
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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