Question

find the values of $a$ and $b$ for which the following system of linear equation has infinite of solution:
$2x-3y=7$
$(a+b)x-(a+b-3)y=4a+b$

Answer 1

Given lines

2x - 3y = 7

(a+b)x-(a+b-3)y = 4a+b

for infinite solution of two given

lines a_{1}x+b_{1}y+c_{1}=0 : a_{2}x+b_{2}y+c_{2} = 0$

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

$\frac{2}{a+b}=\frac{3}{a+b-3}=\frac{7}{4a+b}$

2a+2b-6 = 3a+3b 12a+3b = 7a + 7b -21

a+b = -6 5a - 4b = -21 --(2)

4c + 4b = -24 --(1)

(1)+(2) $\Rightarrow$ 90 = -45 $\Rightarrow$ a = -5

$-5+b=-6=1b=-6+5=-1$

a = -5, b = -1