Question

How do you solve the system of equations `8x+7y = 18` and `3x-5y=22`?

Answer 1

`x = 244/61` and `y = (-122)/61`

Explanation:

Equation 1 => `8x + 7y = 18`

Equation 2 => `3x - 5y = 22`

Multiply Equation 1 by 5 and Equation 2 by 7, we get

Equation 3 => `40x + 35y = 90`

Equation 4 => `21x - 35y = 154`

Adding 3 & 4, we get `61x + 0y = 90 + 154` => `x = 244/61`

Solve in a similar manner to determine y.

Multiply Equation 1 by 3 and Equation 2 by 8, we get

Equation 5 => `24x + 21y = 54`

Equation 6 => `24x - 40y = 176`

Subtract Equation 6 from 5, we get:

`21y + 40 y = 54 -176` => `61 y = -122` => `y = (-122)/61`