Solving by elimination method.
We have the following system of equations:
[tex]\begin{gathered} 5x-y=2 \\ -9x+y=-10 \end{gathered}[/tex]
If we add both equations, we have
[tex]5x-9x=2-10[/tex]
because -y+y=0. That is, we have eliminated y.
Now, by combining similar terms, we obtain
[tex]-4x=-8[/tex]
If we move -4 to the right hand side, we have
[tex]\begin{gathered} x=\frac{-8}{-4} \\ x=2 \end{gathered}[/tex]
Now, we can substitute this value into the first equation. It yields
[tex]\begin{gathered} 5(2)-y=2 \\ 10-y=2 \end{gathered}[/tex]
If we move +10 to the right hand side as -10, we have
[tex]\begin{gathered} -y=2-10 \\ -y=-8 \\ y=8 \end{gathered}[/tex]
Therefore, the answer is x=2 and y=8.
