Solve each system by the addition method.

2x + 4y = 28

X - 2y = 10

Put your answer in ordered pair (x, y) form.

2x + 4y = 28x - 2y = 10

When solving a system by addition, our goal is to cancel out one of the variables by adding the two equations together.

Notice that if we add these two equations together,

neither one of our variables will cancel out.

In this situation, we need to set things up so that when we do add

our two equations together, one of our variables will cancel out.

Notice that we have a 2x in our first equation.

If we had a - 2 in our second equation,

then the x's would cancel out.

In order to create a - 2x in the second equation,

we simply multiply both sides of the second equation by - 2.

So we have (-2) (x - 2y) = (10) (-2).

Rewriting both equations, we have 2x + 4y = 28 and for

our second equation we have - 2x + 4y = - 20.

Now when we add our two equations together,

our x terms will cancel out and were left with 8y = 8.

Dividing both sides by 8, y = 1.

To solve for x, substitute a 1 in for y

in either one of the two equations.

So let's go with our first equation.

If we substitute a 1 in for y, we have 2x + 4 (1) = 28.

4 (1) is 1 according to the identity property of multiplication.

So we have 2x + 4 = 28.

Now subtract 4 from both sides to get 2x = 24.

Now divide both sides by 2 and x = 12.

Now put your answer in the form of the ordered pair {12, 1}.