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Question 126

If the system of equations $$4x + 6y = 11, 2x + ay = 7$$ has no solution, then the value of a is

Solution

Given: $$4x + 6y = 11, 2x + ay = 7$$ have no solution.

For a system of linear equations $$a_1x + b_1y = c_1$$ and $$a_2x + b_2y = c_2$$ to have no solution,

$$\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$$

Comparing with the given equations,

$$\dfrac{4}{2} = \dfrac{6}{a} \neq \dfrac{11}{7}$$

$$a = 3$$

Hence, option C is correct.

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