Question

How do you solve the system of equations `8x + 3y = 58` and `16x - 5y = 50`?

Answer 1

`x = 5` and `y = 6`

Explanation:

First, solve the second equation for `y`:

`16x - 5y - 16x = 50 - 16x`

`-5y = 50 - 16x`

`(-5y)/-5 = (50 - 16x)/-5`

`y = 50/-5 - (16x)/-5`

`y = -10 + (16/5)x`

Next, substitute `-10 + (16/5)x` for `y` in the first equation and solve for `x`:

`8x + 3(-10 + (16/5)x) = 58`

`8x - 30 + (48/5)x = 58`

`8x - 30 + (48/5)x + 30 = 58 + 30`

`8x + (48/5)x = 88`

`(5/5)8x + (48/5)x = 88`

`(40/5)x + (48/5)x = 88`

`88/5x = 88`

`5/88 88/5x = 88 5/88`

`x = 5`

Finally, substitute `5` for `x` in the solution for the second equation and solve for `y`:

`y = -10 + (16/5)5`

`y = -10 + 16`

`y = 6`