Question

Solve simultaneous equation for equation x and y
m+(x+y)+ n(x-y)-(m²+mn+n²)=0
n(x+y)+m(x-y)-(m²-mn+n²)=0

Answer 1

The simultaneous equations are

m(x+y) +n(x-y)-(m²+mn+n²) =0 and

n(x+y) +m(x-y)-(m²-mn+n²) =0.

We have to solve those two equations for x and y.

Now, m(x+y) +n(x-y)-(m²+mn+n²) =0

⇒ x(m + n) + y(m - n) = m² + mn + n² ........... (1)

And, n(x+y) +m(x-y)-(m²-mn+n²) =0

⇒ x(m + n) - y(m - n) = m² - mn + n² ........... (2)

Now, eliminating y from equations (1) and (2) we get,

2x(m + n) = 2(m² + n²)

⇒ (Answer)

Similarly, eliminating x from equations (1) and (2) we get,

2y(m - n) = 2mn

⇒ (Answer)

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