Answer
The solution to this system of equations is $(-1, -\frac{1}{2})$.
Work Step by Step
We can solve for $y$ in terms of $x$ in the second equation so that we can use this value for $y$ to substitute into the first equation. Let us solve for $y$ in the second equation:
$8y = 4x$
Divide both sides by $8$ to solve for $y$:
$y = \dfrac{4x}{8}$
Reduce the fraction by dividing both numerator and denominator by $4$:
$y = \dfrac{x}{2}$
Now, we use this value for $y$ to substitute into the first equation:
$7x + 2(\frac{x}{2}) = -8$
$7x + x = -8$
$8x = -8$
Divide both sides by $8$ to solve for $x$:
$x = -1$
Now that we have a value for $x$, we can substitute it into the second equation to solve for $y$:
$8y = 4(-1)$
$8y = -4$
Divide both sides by $8$ to solve for $y$:
$y = -\dfrac{4}{8}$
Divide both numerator and denominator by $4$ to simplify the fraction:
$y = -\dfrac{1}{2}$
The solution to this system of equations is $(-1, -\frac{1}{2})$.
