Question

If the system of linear equations $\{\begin{array}{c}\frac{1}{2}x-\frac{2}{3}y=7\\ ax-8y=-1\end{array}$ has no solution then the value of constant $a$ is.

• A. $-2$
• B. $-\frac{1}{2}$
• C. $2$
• D. $6$

Answer 1

The correct option is D $6$

If a system of linear equation has no solution then, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Therefore $\frac{\frac{1}{2}}{a}=\frac{-\frac{2}{3}}{-8}$

$\Rightarrow \frac{1}{2a}=\frac{1}{12}$

$\Rightarrow 2a=12$

Hence $a=6$