Alg3.1.10

Solve the following systems of linear equations in x and y $ax+by-a+b=0,bx-ay-a-b=0\,$

Given $ax+by-(a-b)=0,bx-ay-(a+b)=0\,$

Using cross multiplication method,we have

$x=\frac{b_1c_2-b_2c_1}{a_1 b_2-a_2 b_1},y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}\,$

$x=\frac{(b)(-(a+b))-(-a)(-(a-b))}{-a^2+b^2},y=\frac{-(a-b)b+(a+b)a}{-a^2+b^2}\,$

$x=\frac{-ab-b^2-a^2+ab}{b^2-a^2},y=\frac{-ab+b^2+a^2+ab}{b^2-a^2}\,$

$x=\frac{a^2+b^2}{a^2-b^2},y=\frac{a^2+b^2}{b^2-a^2}\,$