To solve this system of equations by addition, our first goal is to cancel
out one of the variables by adding the two equations together.
However, if we add these two equations together right away, nothing
will cancel so we need to set things up so a variable will cancel.
Notice that we have an 2x in our second equation.
If we had a -2x in our first equation, then the x's would cancel out.
In order to create a -2x in the first equation, we simply
multiply both sides of the first equation by -2.
So we have (-2)(x - 2y) = (-4)(-2) which can be rewritten as -2x + 4y = 8.
Now rewrite both equations, as shown below.
Now when we add the equations together, the x terms
will cancel out and we're left with 5y = 15.
Dividing both sides by 5, y = 3.
To solve for x, plug a 3 in for y in either one of our 2 original equations.
So let's go with our second equation.
Plugging a 3 in for y, we get 2x + (3) = 7.
Now subtract 4 from both sides to get 2x = 4.
Dividing both sides by 2, we fid that x = 2.
Since x = 2 and y = 3, our answer is the ordered pair (2, 3).
