Question

ax + by = a - b
bx - ay = a+ b
by elimination ​

Answer 1

$ax + by = a - b \: \: \: ...(i)\\ \\ bx - ay = a+ b \: \: \: ...(ii)$

Multiply equation (i) with a and equation (ii) with b ,

${a}^{2} x + aby = {a}^{2} - ab \: \: \: ...(iii)\\ \\ {b}^{2} x - aby = ab + {b}^{2} \: \: \: ...(iv)$

Adding (iii) and (iv) , we get ,

$( {a}^{2} + {b}^{2} )x = {a}^{2} + {b}^{2} \\ \\ x = 1$

Now , from (i) ,

$ax+by=a−b \\ \\ a+by=a−b\\ \\ by=−b \\ \\ y=−1$

Answer 2

Answer: x = 1, y = -1

Step-by-Step Explanation:

As the answer involves many steps, I’ve taken a pic of my working. Please check the attached photo.