We will solve the problem using the substitution method.
The system of equations to be solved is
[tex]\begin{cases}3x-y=6 \\ -2x+2y=8\end{cases}[/tex]
Notice that the second equation is equivalent to
[tex]\begin{gathered} -2x+2y=8 \\ \Leftrightarrow\frac{1}{2}(-2x+2y)=\frac{1}{2}(8) \\ \Leftrightarrow-x+y=4 \end{gathered}[/tex]
Then,
[tex]\Rightarrow y=4+x[/tex]
We can substitute the last result into the first equation of the system as shown below
[tex]\begin{gathered} 3x-y=6 \\ \Rightarrow3x-(4+x)=6 \\ \Rightarrow3x-4-x=6 \\ \Rightarrow2x=6+4=10 \\ \Rightarrow x=5 \end{gathered}[/tex]
Finally,
[tex]\begin{gathered} \Rightarrow y=4+(5)=9 \\ \Rightarrow y=9 \end{gathered}[/tex]
The answer is (x,y)=(5,9)
