Question

Find values of a and b if x+2y=1 and (a-b)x+(a+b)y=a+b-2 have infinitely many solutions

Answer 1

Answer:

For infinite many solution,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

i.e,

$\frac{a - b}{1} = \frac{a + b}{2} = \frac{a + b - 2}{1}$

1st solve,

$a - b = a + b - 2$

$2b = 2 \: \: \: so \: \: b = 1$

now solve,

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

$2a - 2b = a + b$

$a = 3b = 3 \times 1 = 3$

so a = 3 & b = 1.