Determine the values of a and b for which the given system of linear equations has infinitely many solutions:
2x + 3y = 7and a(x+y) -b(x-y) = 3a + b - 2

2x + 3y = 7 ----------------(1)
a( x + y) - b (x - y) = 3a + b - 2
ax + ay - bx + by = 3a + b - 2
ax -bx + ay + by = 3a + b - 2
(a - b ) x + ( a + b) y = 3a + b - 2 --------------(2)

For Infinetly many solutions

a₁/a₂ = b₁/b₂ = c_1/c₂

2/(a - b) = 3/(a + b) = 7/(3a + b -2)

•  2/(a - b) = 3/(a + b)  

              2​(a + b) = 3 ​(a - b)
             2a + 2b = 3a - 3b
             a - 5b = 0 --------------(3)

•  3/(a + b) = 7/(3a + b -2)      

              3 (3a + b -2) = 7 (a + b)
              9a + 3b - 6 = 7a + 7b
             2a - 4b = 6 ----------(4)
Multiply eq. (3) by 2
        2a - 10b = 0 -----------(5)
On subtracting eq. (5) from eq. (4), we get
6b = 6
b = 1
Put value of "b" in eq (5 ), we get, 
2a - 10(1) = 0
2a = 10
a = 5
Ans. a= 5, b =1