Question

Solve for x and y: mx-ny=m2+n2;x-y=2n

Answer 1

mx - ny = m² + n²
x - y = 2n

From second equation,
x-y=2n
⇒ x = 2n + y

Putting in first equation,
m(2n+y) – ny = m² + n²
⇒ 2mn + (m-n)y = m² + n² 
⇒ (m-n)y = m² + n² – 2mn
⇒ (m-n)y = (m-n)²
⇒ y = (m-n)² / (m-n)
⇒ y = m - n

x = 2n+ y = 2n + m – n
⇒ x = m + n

Answer 2

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