Answer
The solution to this system of equations is $\left(7, \frac{5}{4}\right)$.
Work Step by Step
We want to make it so that with both of the equations, one of the variables is exactly the same except that each equation, the variable will differ in sign; then, we can eliminate that variable.
With this in mind, we see that we can multiply the first equation by $-2$ so that the $x$ terms will only differ in sign:
$(-2)(x + 4y) = (-2)12$
$-2x - 8y = -24$
Thus, the given system of equations is equivalent to:
$-2x - 8y = -24$
$ 2x - 8y = 4$
Add the equations together to eliminate the $x$ variable:
$(-2x-8y)+(2x-8y) = -24+4$
$- 16y = -20$
$y=\frac{-20}{-16}\\
y=\frac{5}{4}$
Now that we have the value for $y$, we can plug it into one of the equations to solve for $x$. Let's plug in the value for $y$ into the first equation:
$x + 4(\frac{5}{4}) = 12$
$x + \frac{20}{4} = 12$
$x + 5 = 12$
Now, we subtract $5$ from both sides of the equation to solve for $x$:
$x = 7$
The solution to this system of equations is $\left(7, \frac{5}{4}\right)$.
