Question

How do you solve the system of equations `x+y=14` and `-x+y=16`?

Answer 1

`(x, y)=(-1, 15)`

Explanation:

The end goal is to get an equation in terms of one variable, which can be solved.

We can solve using substitution. We'll need to pick one of our equations and solve for `x` or `y.` It does not matter which equation is used for this purpose, nor does it matter which variable is solved for.

This is a nice system, solving for either variable in either equation will be equally easy. Let's take `x+y=14`:

`y=14-x`

Now, we can replace all `y` in the other equation, `-x+y=16`, with `14-x:`

`-x+y=16`

`-x+14-x=16`

`-2x=16-14`

`-2x=2`

`x=-1`

To solve for `y,` we can just back-substitute the above result into `y=14-x:`

`y=14-(-1)`

`y=15`

Thus,

`(x, y)=(-1, 15)`