To solve this system of equations, I would use addition.
If you're going to solve a system of equations by addition,
both equations have to be in standard form.
Here, they both are in standard form so we can use addition.
Notice that we have a 5y in the first equation
and a 8y in the second equation.
If we multiply the 5y from the first equation by 8, that would give us 40y and if we multiplied the 8y in the second equation by -5, that would give us -40y.
So we would have a 40y and a -40y and our <em>y</em> terms would cancel.
So let's multiply our first equation by 8 to gives us our 40y and let's multiply our second equation by -5 to gives us our -40y.
Our first equation then becomes -24x + 40y = -72 and
our second equation becomes -20x - 40y = -60.
Now when we add our two equations together, our y's will cancel out.
-24x + -20x is -44x and -72 + -60 is -132.
So we have -44x = -132.
Now dividing both sides by -44, we find that x = 3.
To solve for y, let's plug a 3 back in for x in our first equation
to get -3(3) + 5y = -9 or -9 + 5y = -9.
Adding 9 to both sides, we have 5y = 0 and dividing
both sides of the equation by 5, we find y = 0
So our answer is the ordered pair (3, 0).
