Answer
The solution to this system of equations is $(-2, \frac{1}{2})$.
Work Step by Step
We can solve for $v$ in terms of $u$ in the first equation so that we can use this value for $v$ to substitute into the second equation. Solve for $v$ in the first equation by dividing the entire equation by $4$ to isolate $v$:
$v = \frac{3}{4}u + \frac{8}{4}$
$v = \frac{3}{4}u + 2$
Now, we use this value for $v$ to substitute into the second equation:
$24v=6-3u\\
24\left(\frac{3}{4}u + 2\right) = 6 - 3u$
Distribute and multiply to simplify:
$\frac{72}{4}u + 48 = 6 - 3u$
$18u + 48 = 6 - 3u$
Subtract $48$ from both sides of the equation to move constants to the right side of the equation:
$18u = -42 - 3u$
Add $3u$ to both sides of the equation to move variables to the left side of the equation:
$21u = -42$
Divide both sides by $21$ to solve for $u$:
$u = -2$
Now that we have a value for $u$, we can substitute it into the second equation to solve for $v$:
$24v=6-3u\\
24v = 6 - 3(-2)$
$24v = 6 + 6$
$24v = 12$
Divide both sides by $24$ to solve for $v$:
$v = \frac{1}{2}$
The solution to this system of equations is $(-2, \frac{1}{2})$.
