Question

Solve: ax + by = a - b

bx - ay = a + b

Answer 1

ax+by=a-b
ax=a-b-by
x=(a-b-by)/a

bx-ay=a+b
substituting
b(a-b-by/a)-ay=a+b
ab-b²-b²y/a-ay=a+b
ab-b²-b²y-a²y/a=a+b
ab-b²-(b²+a²)y=a²+ab
-(b²+a²)y=a²+ab-ab+b²
(b²+a²)y=-(a²+b²)
y=-(a²+b²)/a²+b²
y= -1←

substituting value of y
x=a-b-b(-1)/a
x=a-b+b/a
x=a/a
x=1