We are to solve the equations
[tex]\begin{gathered} y=-2x+1 \\ 0.5x-y=4 \end{gathered}[/tex]The equation can be rewritten as
[tex]\begin{gathered} y+2x=1------------\text{equation 1} \\ -y+0.5x=4-----------\text{equation 2} \end{gathered}[/tex]Using substitution method
From equation 1
[tex]y=1-2x--------\text{equation 3}[/tex]Substitute 1 - 2x for y into equation 2
This gives
[tex]\begin{gathered} -(1-2x)+0.5x=4 \\ -1+2x+0.5x=4 \\ -1+2.5x=4 \\ 2.5x=4+1 \\ 2.5x=5 \\ x=\frac{5}{2.5} \\ x=2 \end{gathered}[/tex]Therefore, x = 2
Substitute 2 for x into equation 3
This gives
[tex]\begin{gathered} y=1-2(2) \\ y=1-4 \\ y=-3 \end{gathered}[/tex]Therefore the solution to the equations is
x = 2, y = -3
