Question

For which value's of $a$ & $b$ does the following pair of linear equation have an infinite number of solution
$2x+3y=7$
$(a-b)x+(a+b)y=3a+b-2$

Answer 1

Condition for a pair of linear equation to have an infinite number of solutions

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

$a_1=2$, $b_2=3$, $c_1=7$

$a_2=a-b$, $b_2=a+b$, $c_2=3a+b-2$

$\frac{2}{a-b}=\frac{3}{a+b}=\frac{7}{3a+b-2}$

$2a+2b=3a-3b$

$a=5b$

$7a+7b=9a+3b-6$

$2a-4b=6$

$a-2b=3$

put $a=5b$

5b-2b=3$

$3b=3$

$b=1$

$a=5b$

$a=5\times 1$

$a=5$, $b=1$