If the equations (ax+4y=10) and (6x+8y=25) have no solution, what is the value of (a)?
Answer and explanation
Correct answer: 3
For two linear equations to have no solution, the ratios of the coefficients of both variables must be equal, while the ratio of the constant terms must be different. Thus, \(\frac{a}{6}=\frac{4}{8}=\frac{1}{2}\), which gives \(a=3\). Also, \(\frac{10}{25}=\frac{2}{5}\), which is not equal to \(\frac{1}{2}\); therefore, the two lines are parallel and inconsistent. Exam tip: For ‘no solution,’ first check that the variable-coefficient ratios are equal and then verify that the constant-term ratio is different.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For two linear equations to have no solution, the ratios of the coefficients of both variables must be equal, while the ratio of the constant terms must be different. Thus, \(\frac{a}{6}=\frac{4}{8}=\frac{1}{2}\), which gives \(a=3\). Also, \(\frac{10}{25}=\frac{2}{5}\), which is not equal to \(\frac{1}{2}\); therefore, the two lines are parallel and inconsistent. Exam tip: For ‘no solution,’ first check that the variable-coefficient ratios are equal and then verify that the constant-term ratio is different.
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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