Question

ax+by=a-b, bx-ay=a+b

Answer 1

ax+by=a-b

bx-ay=a+b

abx + b^2 y = ab - b^2
abx - a^2 y = a^2 + ab
now subtract to get
(a^2+b^2)y = b^2-a^2

y = (-b^2-a^2)/(a^2+b^2)
y = -1

a^2x+aby = a^2-ab
b^2x-aby = ab+b^2

x = (a^2+b^2)/(a^2+b^2)
x = 1