Since you have y alone on one side of the equation......
Use substitution and plug in 1/2x-4 for y in the other equation.
[tex]3x+2(1/2x-4)=23\\[/tex]
Distribute
[tex]3x+x-8=23[/tex]
Combine like terms
[tex]4x-8=23[/tex]
Add 8 to both sides
[tex]4x=31[/tex]
Divide by 4
and [tex]x=31/4[/tex]
Plug this value in for x
[tex]31/4*1/2-4=y[/tex]
Simplify
[tex]31/8-4=y[/tex]
Multiply everything by 8 and simplify
[tex]31-32=8y\\-1=8y[/tex]
Divide.....
[tex]y=-1/8[/tex]
Your answers are:
[tex]y=-1/8\\x=31/4[/tex]
