Question

solve the equation
mx-ny=m^2+n^2
x+y=2m

Answer 1

Given Equation is mx - ny = m^2 + n^2   ----------- (1)

Given Equation is x + y = 2m.   --------- (2).

Multiply Equation (2) with n on both sides, we get

nx + ny = 2mn    ------------------ (3)

On solving (1) & (2), we get

nx + ny + mx - ny = m^2 + n^2 + 2mn

nx + mx = (m + n)^2

(m + n)x = (m + n)^2

x = $\frac{(m + n)^2}{m + n}$

x = m + n.           ----------------- (4)


Substitute (4) in (2), we get

m + n + y = 2m

y = 2m - m - n

y = m - n.


Therefore the value of x = (m + n) and y = (m - n).


Hope this helps!