# How do I use elimination to find the solution of the system of equations y=−2x−4 and y+4=−2x?

Sep 17, 2014

This is actually a bit of a trick question since the two equations are equivalent.

If you solve $y + 4 = - 2 x$ for $y$ you'll get $y = - 2 x - 4$ which is the same as the first equation mentioned in the question.

In a case like this, where you have more variables than equations (there are 2 variables- $x$ and $y$, but only equation of $y = - 2 x - 4$) there will actually be infinitely many solutions. You can keep plugging in infinitely many values for $x$ and keep getting outputs for $y$.

Notice that $y = - 2 x - 4$ is just the equation of a straight line in the form of $y = m x + b$, where the line is continuous for all real numbers (so for all $x$). That's why this this isn't really a "system". The two equations in the question equal each other, hence there is only one net equation, In that net equation, you can have any value for $x$ (or $y$) plugged in and a different solution can be found each time.