Question

solve for x and y: ax+by=a-b and bx-ay=a+b

Answer 1

[math]ax+by=a-b \cdots (1)[/math]

[math]bx-ay=a+b \cdots (2)[/math]

[math](1)×a \implies a^2x+aby = a^2-ab \cdots (3)[/math]

[math](2)×b \implies b^2x-aby = ab+b^2 \cdots (4)[/math]

Adding the like terms of both equations,

[math](a^2+b^2)x = a^2-ab+ab+b^2[/math]

[math]\implies (a^2+b^2)x = a^2+b^2[/math]

[[math]\because \text{+aby and -aby gets cancelled}[/math]]

[math]\implies x = \dfrac{a^2+b^2}{a^2+b^2}[/math]

[math]\implies \boxed{x = 1}[/math]

Substitute x=1 in equation (1).

[math]a(1) + by = a -b[/math]

[math]a + by = a -b[/math]

[math]by = a-b-a[/math]

[math]by = -b[/math]

[math]y = \dfrac{-b}{b}[/math]

[math]\implies \boxed{y=-1}[/math]

Therefore, solution is [math]\hspace{1mm} (x,y) = (1,-1)[/math]

Answer 2

Your answer is x = 1 & y = - 1