What is the value of (a) for the equations (ax+4y=10) and (6x+8y=25) to have no solution?
Answer and explanation
Correct answer: 3
Two linear equations have no solution when \,\(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \,\(\frac{a}{6}=\frac{4}{8}=\frac{1}{2}\), so \,\(a=3\). Also, \,\(\frac{10}{25}=\frac{2}{5}\ne\frac{1}{2}\), so the two lines are distinct and parallel, giving no solution. Exam tip: first equate the ratios of the x- and y-coefficients, then check the constant-term ratio.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Two linear equations have no solution when \,\(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \,\(\frac{a}{6}=\frac{4}{8}=\frac{1}{2}\), so \,\(a=3\). Also, \,\(\frac{10}{25}=\frac{2}{5}\ne\frac{1}{2}\), so the two lines are distinct and parallel, giving no solution. Exam tip: first equate the ratios of the x- and y-coefficients, then check the constant-term ratio.
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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