Question

Solve the simultaneous linear equation using substitution method:

mx - ny = m^2 + n^2

x + y = 2m

Answer 1

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

Addding 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

Hope that helped... Thank you!