Question

Express the positive value of ${}^{\prime }{a}^{\prime }$ if the pair linear equation $ax+3y-a=0$ and $6x+ay-6=0$ have infinitely many solutions.

Answer 1

We have,

Equation of line

$ax+3y-a=0......\left(1\right)$

$6x+ay-6=0......\left(2\right)$

Comparing that,

$a_{1}x+b_{1}y+c_{\stackrel{`}{}1}=0$

$a_{2}x+b_{2}y+c_2=0$

Then,

$a_1=a$

$b_1=3$

$c_1=-a$

$a_2=6$

$b_2=a$

$c_2=-6$

Its many infinite many solutions

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

$\Rightarrow \frac{a}{6}=\frac{3}{a}=\frac{-a}{-6}$

$\Rightarrow \frac{a}{6}=\frac{3}{a}=\frac{a}{6}$

We have,

$\frac{a}{6}=\frac{3}{a}$

$a^2=18$

$a=\pm \sqrt{18}$

$a=\pm \sqrt{3\times 3\times 2}$

$a=\pm 3\sqrt{2}$

Hence, this is the answer.