We have the system of equations:
[tex]\begin{gathered} x-y=2 \\ y=4-2x \end{gathered}[/tex]We can solve by substitution, using the information already given by the second equation.
We can replace y in the first equation and solve for x:
[tex]\begin{gathered} x-y=2 \\ x-(4-2x)=2 \\ x-4+2x=2 \\ x+2x=2+4 \\ 3x=6 \\ x=\frac{6}{3} \\ x=2 \end{gathered}[/tex]Then, we can find y using the second equation as:
[tex]y=4-2x=4-2\cdot2=4-4=0[/tex]Answer: x=2 and y=0
