Question

For what value of a and b would the following pair of linear equations have infinite solutions.
-3x + 2y =9, (a + b - 1)x-(a - b+3)y=-18​

Answer 1

Answer:

for infinite solutions, the condition is a1/a2=b1/b2≠c1/c2

so, a+b-1=-3

then, a=-3+1-b

for 2^nd eq^n -(a-b+3) =2

putting value of a in 2^nd eq^n,

-(-3+1-b-b+3) =2

-(1-2b) =2

-1+2b=2

2b=2+1

b=3/2 we get the value of b.

now, put the value of b in eq^n 1^st, we get

a=-3+1-3/2

a=-6+2-3/2

a=-7/2

so, the value of a is -7/2 and b is 3/2