Linear Equations (C10)

For what values of m and n the following system of linear equations has infinitely many solutions.
3x + 4y = 12
(m + n)x + 2(m – n)y = 5m – 1

Answer

For infinitely many solutions,

3/(m+n) = 4/2(m – n) = –12/ –(5m – 1)

m – 5n = 0 ...(1)

m – 6n = –1 ...(2)

Solving (1) and (2) we get,

m = 5, n = 1