Question

How do you solve 4x - y = -5 and -2x + 3y = 10?

Answer 1

`{(x=-1/2), (y=3):}`

Explanation:

Your system of equations looks like this

`{(4x-y = -5), (-2x + 3y = 10):}`

Multiply the second equation by `2` to get

`{(4x-y = -5), (-4x + 6y = 20):}`

Notice that if you add the left-hand side of the equations and the right-hand sides of the equations separately, you can eliminate the `x`-term.

This will allow you to find the value of `y`, since you'll be left with one equation with one unknown, `y`.

`{(4x-y = -5), (-4x + 6y = 20):}`
`stackrel("--------------------------------------------")`
`color(red)(cancel(color(black)(4x))) - y - color(red)(cancel(color(black)(4x))) + 6y = -5 + 20`

`5y = 15 implies y = color(green)(3)`

Now take the value of `y` into one of the two original equations to solve for `x`

`4x - 3 = -5`

`4x = -2 implies x = color(green)(-1/2)`