Given the system of equations:
[tex]\begin{gathered} 2x+2y=6 \\ 2x-2y=6 \end{gathered}[/tex]we can solve it using elimination by directly adding both equations to get the following:
[tex]\begin{gathered} 2x+2y=6 \\ 2x-2y=6 \\ ---------- \\ 4x=12 \\ \Rightarrow x=\frac{12}{4}=3 \\ x=3 \end{gathered}[/tex]now that we have that x=3, we can find y using this value on any of the two equations:
[tex]\begin{gathered} 2x+2y=6 \\ x=3 \\ \Rightarrow2(3)+2y=6 \\ \Rightarrow6+2y=6 \\ \Rightarrow2y=6-6=0 \\ \Rightarrow2y=0 \\ y=0 \end{gathered}[/tex]therefore, the solution of the system is (3,0)
