Find x and y in terms of a and b. Pls help!!?

Question

ax-by=a^2+b^2
2bx-ay=2b^2+3ab-a^2
Ans: x=a +b
y=a - b

Answer 1

ax - by = a^2 + b^2 ......(1)
2bx - ay = 2b^2 + 3ab - a^2 ........(2)

(1) * a:
a^2x - aby = a^3 + ab^2 ........(3)
(2) * b:
2b^2x - aby = 2b^3 + 3ab^2 - a^2b .......(4)

(3) - (4):
(a^2 - 2b^2)x = a^3 + ab^2 - 2b^3 - 3ab^2 + a^2b
(a^2 - 2b^2)x = a^3 - 2ab^2 + a^2b - 2b^3
(a^2 - 2b^2)x = a^2(a + b) - 2b^2(a + b)
(a^2 - 2b^2)x = (a^2 - 2b^2)(a + b)
Hence, provided a^2 - 2b^2 <> 0:
x = a + b.

Substitute for x in (1):
a(a + b) - by = a^2 + b^2
by = a^2 + ab - a^2 - b^2
by = ab - b^2
Hence, provided b <> 0:
y = a - b.