Given the system of equations:
[tex]\begin{cases}y-2x=-5 \\ y-x=-3\end{cases}[/tex]notice that we can multiply the second equation by -1 to get the following:
[tex]\begin{gathered} -1\cdot(y-x=-3) \\ \Rightarrow-y+x=3 \end{gathered}[/tex]next, we can add both equations to get the following:
[tex]\begin{gathered} y-2x=-5 \\ -y+x=3 \\ --------- \\ 0y-x=-2 \\ \Rightarrow x=2 \end{gathered}[/tex]now that we have that x = 2, we can use this value on the first equation to get the value of 'y':
[tex]\begin{gathered} x=2 \\ \Rightarrow y-2(2)=-5 \\ \Rightarrow y-4=-5 \\ \Rightarrow y=-5+4=-1 \\ y=-1 \end{gathered}[/tex]therefore, the solution of the system of equations is (2,-1)
