Question

How do you solve the system of equations `-2x + 2y = - 14` and `7x + 10y = 15`?

Answer 1

Use elimination to cancel one variable and solve the system for the other variable.

Explanation:

We can scale the first equation by `5` to get the same `y` value as the second one, `10y`.

So, `(-2x + 2y = -14)*5 = -10x+10y=-70`

`eq1 = -10x+10y=-70`
`eq2 = 7x+10y=15`

Now we can subtract both equations together, `eq1- eq2 = -17x = -85`, so `x=85/17 = 5`

We substiture this value of `x` back into the original equations to find `y`, so `-2(5) + 2y = -14 -> 2y = -4 -> y = -2`

The solution is `x = 5, y = -2`