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 —

2*x* + 3*y* = 7 ......(1)

a*x* + *ay* – *bx* + *by* = 3*a* + *b* – 2

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

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

2*x* + 3*y* – 7 = 0 ......(3)

(*a* – *b*) *x* + (*a* + *b*) *y* + (–3*a* – *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

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