We hahve to solve the following system of equations:
[tex]\begin{gathered} 3x+2y=15 \\ x=y+15 \end{gathered}[/tex]We can use the second equation to replace x in the first equation and solve for y as:
[tex]\begin{gathered} 3x+2y=15 \\ 3(y+15)+2y=15 \\ 3y+45+2y=15 \\ 5y=15-45 \\ 5y=-30 \\ y=\frac{-30}{5} \\ y=-6 \end{gathered}[/tex]Knowing y we can calculate x as:
[tex]\begin{gathered} x=y+15 \\ x=-6+15 \\ x=9 \end{gathered}[/tex]Answer: (x,y) = (9,-6)
