Respuesta :
Given the systems of equation
[tex]\begin{gathered} 5x-y=4 \\ 2x-y=-1 \end{gathered}[/tex]We want to solve it using the substitution method. The first step is to get one equation from the systems of equations and solve it in terms of x. I will choose the second equation in this case. We have
[tex]\begin{gathered} 2x-y=-1 \\ -y=-1-2x \\ y=1+2x \end{gathered}[/tex]Put this equation on the first equation present in the system of equations and solve for x. We have
[tex]\begin{gathered} 5x-(1+2x)=4 \\ 5x-1-2x=4 \\ 5x-2x=4+1 \\ 3x=5 \\ x=\frac{5}{3} \end{gathered}[/tex]Use this value of x and substitute it on one of the equations on the system of equations to solve for the value of y. In this case, I will be using equation 2. We have
[tex]\begin{gathered} y=1+2(\frac{5}{3})_{} \\ y=1+\frac{10}{3} \\ y=\frac{3+10}{3} \\ y=\frac{13}{3} \end{gathered}[/tex]