Respuesta :
We need to solve the system of equations:
[tex]\begin{gathered} 3x-2y=25 \\ 5x+10y=-25 \end{gathered}[/tex]We can rewrite the first equation as:
[tex]\begin{gathered} 3x-2y-3x=25-3x \\ \\ -2y=25-3x \\ \\ (-1)(-2y)=(-1)(25-3x) \\ \\ 2y=3x-25 \\ \\ y=\frac{3x-25}{2} \end{gathered}[/tex]Now, we can replace y with the above expression in the second equation. We obtain:
[tex]\begin{gathered} 5x+10\cdot\frac{3x-25}{2}=-25 \\ \\ 5x+\frac{10}{2}(3x-25)=-25 \\ \\ 5x+5(3x-25)=-25 \\ \\ 5x+15x-125=-25 \\ \\ 20x-125+125=-25+125 \\ \\ 20x=100 \\ \\ x=\frac{100}{20} \\ \\ x=5 \end{gathered}[/tex]Now, we use x = 5 to find y:
[tex]\begin{gathered} y=\frac{3(5)-25}{2} \\ \\ y=\frac{15-25}{2} \\ \\ y=-\frac{10}{2} \\ \\ y=-5 \end{gathered}[/tex]Therefore, the solution to this system is the ordered pair (5, -5).
