How do you solve -x-6y=-18 and x-6y=-6 using the addition and subtraction method?

Oct 24, 2014

The answer is $x = 6$ and $y = 2$

The easiest way to solve such systems of equations using the elimination (or as you put it "addition and subtraction") method, is to write out our two equations, one below the other, and see how we can cancel out a variable to bring it down to a one-variable equation.

Here we have:

$- x - 6 y = - 18$
$x - 6 y = - 6$

Think of this as one of those addition or subtraction problems you did back in elementary school, with the number stacked on each other like this for you to work with. You have two paths of action here: you can either add the two equations, or subtract one from the other. Which one will you chose, in order to eliminate a variable?

In this case, both methods would work. If we added, we'd end up eliminating the $x$

[x + (-x) = 0],

and if we subtracted, we'd end up eliminating the $y$

$\left[- 6 y - \left(- 6 y\right) = 0\right]$.

So for this particular problem the course of action is up to you. I'm going to go with addition, since I just like adding better (it's more straightforward).

$\left[- x - 6 y = - 18\right]$
$+ \left[x - 6 y = - 6\right]$

=> $- 12 y = - 24$

$y = 2$

Now that we have one variable solved, we can plug it back into one of our original equations and solve for the other one. Again, it's completely up to you which one to use, but I'm going to use the second one:

$x - 6 \left(2\right) = - 6$

$x - 12 = - 6$

$x = 6$

So our solution to this system is the coordinate $\left(6 , 2\right)$, meaning that if we graphed these two lines, they would intersect at that coordinate.

Hope that helped :)