Q. 2 B3.6( 5 Votes )

# Solve the following pair of linear equations by substitution method:x + y = 2mmx — ny = m2 + n2

Given equations are

x + y = 2m …(i)

mx – ny = m2 + n2 …(ii)

From eqn (i), x = 2m – y …(iii)

On substituting x = 2m – y in eqn (ii), we get

m(2m – y) – ny = m2 + n2

2m2 – my – ny = m2 + n2

– y(m + n) = m2 – 2m2 + n2

– y(m + n) = – m2 + n2  y = – (n – m) = m – n

Now, on putting y = m – n in eqn (iii), we get

x = 2m – (m – n)

x = 2m – m + n

x = m + n

Thus, x = m + n and y = m – n is the required solution.

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