Answer
The solution set is $\{(4, 6)\}$.
Work Step by Step
In order to remove fractions, we will multiply the first equation by $6$ and the second equation by $2$.
The new system of equations is:
$$3x+2y=24 ~~~(1) \\ 3x+3y=30 ~~~(2)$$
Now, multiply equation $(2)$ by $-1$ to obtain:
$$-3x-3y=-30 ~~~(3)$$
Add equations $(1)$ and $(3)$ to eliminate $x$ and then solve for $y$.
$$(3x+2y)+(-3x-3y)=24+(-30) \\ -y=-6 \\ y=6$$
Plug $y=6$ into the first equation then solve for $x$ to obtain:
$$3x+(2)(6)=24 \\ 3x+12=24\\ 3x=24-12 \\ 3x=12\\x=4$$
Thus, the solution set is $\{(4, 6)\}$.
