Solve

 Dear Student 

Solving by Cross multiplication

ax + by = a – b

 bx – ay = a + b

    Here, a₁ = a                    b₁  = b

       a₂ = b                             b₂ = -a

     c₁ = a – b                        c₂ = a + b

However Elimination method is easy to apply here as shown below

ax + by = a - b    ....(1)

bx - ay = a + b    .....(2)

Cross multiply (1) by b and (2) by a,

abx  + b²y = ab - b²

abx - a²y = a² + ab

Now subtracting these two, we get

(a²+ b²)y = -(a²+ b²)

y = -1,

Using this in equation (1),

ax - b = a - b

we get x = 1.

Regards,

Team,

TopperLearning.