Question

Find the value of $a$ for which the following system of equations will have an infinite number of solutions:
$2x-y=8$, $6x-3y=4a$

• A. 2
• B. 6
• C. 8
• D. 24
• E. 32

Answer 1

The correct option is B 6

If a system has infinite number of solution, then

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

$2x-y=8$

Here$a_1=2,b_1=-1,c_1=8$

$6x-3y=4a$

Here $a_2=6,b_2=-3,c_2=4a$

$\therefore \frac{2}{6}=\frac{-1}{-3}=\frac{8}{4a}$

$\Rightarrow \frac{1}{3}=\frac{8}{4a}$

$\Rightarrow 4a=8\times 3$

$\Rightarrow 4a=24$

$\Rightarrow a=\frac{24}{4}=6$