Question

For what value of a and b will the following pair of equations have infinite solution.

x+2y = 1

(a-b)x + (a+b)y =2a-b+1

Answer 1

If the
a1x+b1Y+ c1 = 0,
a2x+b2y+c2 = 0 system has infinitely many solutions then
a1/a2 = b1/b2 = c1/c2.
x + 2y = 1 ,
​​​​​​(a–b)x +(a + b)y =(2a-b+1)
1 / (a – b) = 2 / (a + b) =
1 / (2a-b+1)
⇒ 1 / (a – b) = 2 / (a + b)
⇒ (a + b) = 2 (a - b)
⇒ a -3b = 0 -----------(1)
⇒ 1 / (a – b) = 1 / (2a-b+1)
⇒ (a – b) = (2a-b+1)
a=2a+1
2a-a=-1
a=-1
Substituting value of a in equation (1)
a-3b=0
-1-3b=0
3b=-1
b=-1/3