We have the system of equations:
[tex]\begin{gathered} -3x+2y=16 \\ 2x+y=1 \end{gathered}[/tex]We have to solve by substitution. We will clear y from the second equation and replace it in the first equation. Then solve for x:
[tex]\begin{gathered} 2x+y=1 \\ y=1-2x \end{gathered}[/tex][tex]\begin{gathered} -3x+2y=16 \\ -3x+2(1-2x)=16 \\ -3x+2-4x=16 \\ -7x+2=16 \\ -7x=16-2 \\ -7x=14 \\ x=\frac{14}{-7} \\ x=-2 \end{gathered}[/tex]Now we can solve for y as:
[tex]y=1-2x=1-2(-2)=1-(-4)=1+4=5[/tex]Answer: x=-2 and y=5