The solve a system of equations using the substitution method, we fisrt need to isolate one of the variables in either of the equations. Let's pick the first one and isolate y:
[tex]\begin{gathered} 5x-y=4 \\ 5x-4=y \\ y=5x-4 \end{gathered}[/tex]Now, we can input this equation into the second one:
[tex]\begin{gathered} 2x-y=-1 \\ 2x-(5x-4)=-1 \\ 2x-5x+4=-1 \\ -3x+4=-1 \\ -3x=-5 \\ x=\frac{-5}{-3} \\ x=\frac{5}{3} \end{gathered}[/tex]Now, we can input the value of x into the first equation:
[tex]\begin{gathered} y=5x-4 \\ y=5\cdot\frac{5}{3}-4 \\ y=\frac{25}{3}-\frac{12}{3} \\ y=\frac{25-12}{3} \\ y=\frac{13}{3} \end{gathered}[/tex]So the answer is x = 5/3 and y = 13/3
