Question

$\frac{1}{3}x-\frac{1}{6}y=4$
$6x-ay=8$
In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$

• A. $\frac{1}{3}$
• B. $1$
• C. $3$
• D. $0$

Answer 1

The correct option is C $3$

$\frac{1}{3}x-\frac{1}{6}y=4$

$6x-ay=8$

condition for no solution

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

$\frac{\frac{1}{3}}{6}=\frac{\frac{-1}{6}}{-a}\ne \frac{4}{8}$

$6a=6\times 3$

$a=3$