Answer
The solution to this system of equations is $(-1, -2)$.
Work Step by Step
First, we rewrite the equations so that the variables are on one side while the constant is on the other:
For the first equation, we subtract $8y$ from each side of the equation to shift all variables to one side of the equation:
$10 = 6x - 8y$
Let us rewrite so variables are on the left and the constant is on the right:
$6x - 8y = 10$
For the second equation, we just flip the $x$ and $y$ terms so that the $x$ term appears first in the equation:
$-4x + 8y = -12$
We now can see that in the two equations, the $y$ terms are exactly the same except they have opposite signs. If we add these two equations together, we can eliminate the variable $y$ and just deal with one variable instead of two.
Let us combine the two equations:
$ 6x - 8y = 10$
$-4x + 8y = -12$
Let us add the two equations together to come up with a single equation:
$2x = -2$
Divide each side by $2$ to solve for $x$:
$x = -1$
Now that we have the value for $x$, we can plug it into one of the equations to solve for $y$.
Let us plug in the value for $x$ into the first equation:
$8y + 10 = 6(-1)$
Multiply first, according to order of operations:
$8y + 10 = -6$
Now, we subtract $10$ from both sides of the equation to isolate constants to the right side of the equation:
$8y = -16$
Divide both sides by $8$ to solve for $y$:
$y = -2$
The solution to this system of equations is $(-1, -2)$.
