What is the correct conclusion by observing (14x-10y=36) and (7x-5y=19)?
Answer and explanation
Correct answer: No solution
For the coefficients, \(\frac{14}{7}=\frac{-10}{-5}=2\), but the ratio of the constant terms is \(\frac{36}{19}\), which is not 2. Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), so the two lines are parallel and distinct and have no common solution. Exam tip: when the first two ratios are equal but the constant-term ratio is different, choose ‘no solution’.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
For the coefficients, \(\frac{14}{7}=\frac{-10}{-5}=2\), but the ratio of the constant terms is \(\frac{36}{19}\), which is not 2. Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), so the two lines are parallel and distinct and have no common solution. Exam tip: when the first two ratios are equal but the constant-term ratio is different, choose ‘no solution’.
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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