Question

solve the simultaneous equation. 1) m(x+y) +n(x-y)-(m²+mn+n²) =0 2) n(x+y) +m(x-y)-(m²-mn+n²) =0​

Answer 1

$x = \frac{m^{2} + n^{2}}{m + n}$ and $y = \frac{mn}{m - n}$

Step-by-step explanation:

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)

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

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

2y(m - n) = 2mn

⇒ $y = \frac{mn}{m - n}$ (Answer)