Question

How do you solve `x + 2y = 7` and `2x - 3y = -5`?

Answer 1

You could solve using substitution.

Explanation:

`x + 2y = 7`
`2x -3y = -5`

We can take one of these equations and solve for one variable, and plug that into the variable in the other equation. Let's use the first equation.

`x + 2y = 7` (We are solving for x)
`x = 7 - 2y` (We now have `x`, so we can plug this into `x` in the other equation)

`2x - 3y =-5`
`2(7 - 2y) - 3y =-5` (Plug in `7 - 2x` from the other equation)
`14 - 4y -3y = -5` (Distribute)
`-7y = -19`
`y = 19/7` (We have the solution for `y`, time to find `x`)

`x + 2(19/7) = 7` (Plug in `y`)
`x + 38/7 = 7`
`x = 11/7` (We have the x value)

The solutions are: `x = 11/7`, and `y = 19/7`.