Solve: mx – ny = m^2 + n^2 and x + y = 2m

Solve: mx – ny = m^2 + n^2 and x + y = 2m [Question Number 4(i) in ML Aggarwal Book Class 9 Chapter 5 Exercise 5.1]

mx – ny = m² + n² –(i)

x + y = 2m –(ii)

From equation (ii) we get,

y = 2m-x —(iii)

Substituting the value of y in equation (i) we get,

mx-n(2m-x)=m²+n²

⟹ mx-2mn+nx =m²+n²

⟹mx+nx=m²+n² +2mn

⟹x(m+n)=(m+n)²

⟹ x=$\frac{(m + n)^2}{(m + n)}$

⟹ x= (m+n)

Now from equation (iii) we get,

y =2m- (m+n) [as x= (m+n)]

⟹ y=2m-m-n

⟹ y= (m-n)

∴ Required Solutions are x =(m+n) and y=(m-n).