We have two unknowns (x and y) and 2 equations.
We will clear one unknown in the first equation and then replace it in the second.
Then, we can solve for the other variable and solve backwards.
The first equation is:
[tex]\begin{gathered} x-3y=-8 \\ x=3y-8 \end{gathered}[/tex]We replace the value of x in the second equation:
[tex]\begin{gathered} 3x+2y=31 \\ 3(3y-8)+2y=31 \\ 9y-24+2y=31 \\ 11y=31+24 \\ 11y=55 \\ y=\frac{55}{11} \\ y=5 \end{gathered}[/tex]Then, with y=5, we can calculate the value of x:
[tex]x=3y-8=3\cdot5-8=15-8=7[/tex]The solution (x,y) is (7,5). The answer is Option D.
