Question

For what values of $a$ does each of the following system of equations have an infinite number of solutions?
$3x+ay=3,ax+3y=3$

Answer 1

Given system of equations are

$3x+ay=3$

$ax+3y=3$

For a system of equations to have infinite no. of solutions

$a_{1}x+b_{1}y=c_1$

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

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

Here $\frac{a_1}{a_2}=\frac{3}{a}$

$\frac{b_1}{b_2}=\frac{a}{3}$

$\frac{c_1}{c_2}=\frac{3}{3}$

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

$⟹a=3$