Question

For which values of a and b will the following pair of linear equations have infinitely many solutions x+2y =1 and (a-b)x +(a+b)y =a+b-2

Answer 1

Answer:

Step-by-step explanation:  We are given to find the values of a and b for which the following pair of linear equations will have infinitely many solutions :

We know that

for a system of linear equations to have infinitely many solutions, the coefficients of the unknown variables (x and y) and the constant terms must be in proportion.

So, for the given system, we must have

We have from above that

and

Again, substituting the value of b in equation (i), we get

Thus, the required values are  a = 3  and  b = 1.