Respuesta :
We can solve the system of equations:
[tex]\begin{gathered} y=x+8 \\ x+y=2 \end{gathered}[/tex]by elimination method.
If we multiply the first equation by -1, we have the following equivalent system:
[tex]\begin{gathered} -y=-x-8 \\ x+y=2 \end{gathered}[/tex]If we add both equation, we obtain
[tex]x=-x-8+2[/tex]because -y+y=0. Since -8+2=-6, we have
[tex]x=-x-6[/tex]Now, we must move -x to the left hand side as +x. It yields,
[tex]\begin{gathered} x+x=-6 \\ 2x=-6 \\ x=\frac{-6}{2} \\ x=-3 \end{gathered}[/tex]Now, we can substitute this value into the first equation. It gives
[tex]\begin{gathered} y=-3+8 \\ y=5 \end{gathered}[/tex]Then, the answer is x=-3 and y=5.
