Hello there. To solve this question, we'll have to remember some properties about system of equations.
Given the system:
[tex]\begin{cases}2x-y=1 \\ -3x+y=-5\end{cases}[/tex]We'll solve it by the addition method. Notice in the first equation we have - y, while we have a + y on the second equation.
Adding both equations, we have:
[tex]\begin{gathered} 2x-y-3x+y=1-5 \\ -x=-4 \end{gathered}[/tex]Multiply both sides of the equation by a factor of (-1)
[tex]x=4[/tex]Plugging this value in any of the two equations, we get:
[tex]\begin{gathered} 2\cdot4-y=1 \\ 8-y=1 \end{gathered}[/tex]Add y - 1 on both sides of the equation
[tex]\begin{gathered} 8-y+y-1=1+y-1 \\ y=7 \end{gathered}[/tex]Therefore the ordered pair that is solution for this system of equation is:
[tex](x,y)=(4,7)[/tex]