Question

Find the value of which the following system of linear equation has infinite no.of solutions 2x+3y=7,a(x+y) - b ( x-y)= 3a+b-2

Answer 1

Answer:

The required values are a=5 and b=1

Step-by-step explanation:

If the system of equations

$a_1\:x+b_1\:y+c_1=0$

$a_2\:x+b_2\:y+c_2=0$ has infinitely many solutions , then

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

Given: The equations

2x + 3y -7 =0

(a-b)x + (a+b)y -(3a+b-2) =0 has infinitely many solutions

Then,

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

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

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

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

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

$a=5b$.......................(1)

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

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

$2a-4b-6=0$

$a-2b-3=0$.................(2)

using (2) in (1) we get

$5b-2b-3=0$

$3b=3$

$b=1$

put b=1 in (1)

$a=5(1)$

$a=5$