This is known as a system of equations. For this system, we are going to use substitution, since you already know what y is equal to.
As you can see, #y=-1/2x-5#. Since we have #y# directly set equal to something, we can substitute it in for #y# anywhere we want. In this case we will substitute it in for #y# in your first equation. #x-2y=2 => x-2(-1/2x-5)=2#
Through algebraic equation steps, we can simplify the equation to be #x+x-10=2#, and solve the equation for #x=6#.
Now that we have the #x# value, we can substitute it in to the #y# equation.
#y=-1/2(6)-5#
When simplified, you get #y=-3-5#, or #y=-8#. And remember, if you'd like to check your answer, simply plug your numbers back in for the variables.
#y=-1/2x-5 => (-8)=-1/2(6)-5#, and when simplified, #-8=-8#.
