Question

Solve for x and y using elimination method :
mx - ny = m2 + n2
x + y = 2m​

Answer 1

Answer:

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Step-by-step explanation:

mx - ny = m2 + n2

⇒  mx - ny = m2 + n2 +2mn - 2mn

⇒  mx - ny = (m + n)2 - 2mn  [identity a2 + 2ab +b2 = (a+b)2] → 1

x + y = 2m  → 2

Substituting eq. 2 in eq. 1.

mx - ny = (m + n)2 - (x + y)n

mx - ny = (m + n)2 - nx - ny

Adding ny to both sides, you get:

mx = (m + n)2 - nx

mx + nx = (m + n)2

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

Dividing both sides by (m + n), you get:

x = m + n

Substituting x = m + 2 in eq. 1.

(m + n) + y = 2m

y = 2m - m - n

y = m - n

Therefore, x = m + 2, y = m - n