Question

For what value of $a$, the lines $2x+3y=3$ and $ax+12y=12$ will have an infinite number of solutions?

• A. $8$
• B. $-8$
• C. $4$
• D. $-4$

Answer 1

The correct option is A $8$

Given lines:
$2x+3y=3$,
$ax+12y=12$
Write the above lines in the form of $y=mx+b$, where $m=$ slope and $b=$ intercept.
So,
$2x+3y=3$
$\Rightarrow y=-\frac{2}{3}x+\frac{3}{3}$
$=\frac{-2}{3}x+1...\left(1\right)$
And
$ax+12y=12$
$\Rightarrow y=-\frac{a}{12}x+\frac{12}{12}$
$=-\frac{a}{12}x+1...\left(2\right)$

Note: For infinite solutions, slopes and intercept must be same.
From line $1$ and $2$, equating their slopes
$-\frac{a}{12}=-\frac{2}{3}$
$-a\times 3=-2\times 12$, (by cross multiplication)
Dividing both side by $-3$
$\frac{-a\times 3}{-3}=\frac{-2\times 12}{-3}$
$a=2\times 4$
$a=8$
Answer:
$a=8$