Question

Solve in the substitution method pleasex - 2y = -5x + 5y = 2

Answer 1

To solve the system of equations:

`\begin{gathered} x-2y=-5 \\ x+5y=2 \end{gathered}`

by the substiturion method we need to solve one of the equations for one of the variables, then we substitute this value in the other equation and solve for the remaining variable. Let's apply this method to the system.

First we solve the first equation for x:

`x=2y-5`

now we plug this value in the second equation:

`\begin{gathered} 2y-5+5y=2 \\ 7y=5+2 \\ 7y=7 \\ y=(7)/(7) \\ y=1 \end{gathered}`

Hence y=1. Once we have the value of y we substiute it in the equation for x:

`\begin{gathered} x=2(1)-5 \\ x=2-5 \\ x=-3 \end{gathered}`

Therefore the solution of the system is x=-3 and y=1