For what values of a and b does the following pair of linear equations has a infinite number of solutions: 2x+3y=7; a(x+y)-b(x-y)=3a+b-2.

The given system of equations is —

2x + 3y = 7  ......(1)

ax + ay – bx + by = 3a + b – 2

i.e. (a – b) x + (a + b) y + (–3a – b + 2) = 0  ......(2)

Equations (1) and (2) can be written as —

2x + 3y – 7 = 0 ......(3)

(a – b) x + (a + b) y + (–3a – b + 2) = 0  ......(4)

It is given that the system has infinitely many solution.

So,

from first two terms, we get —

from second and third term, we get —

Solving (1) and (2), we get —

a = 5 and b = 1