Question

Solve the system of linear equations by substitution:x - y = -2 and 3x - y = 2

Answer 1

To solve the system by substitution, isolate one variable from one equation and substitute the expression obtained for that variable into the other equation.

`\begin{gathered} x-y=-2 \\ 3x-y=2 \end{gathered}`

Isolate x from the first equation:

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

Substitute x=y-2 into the second equation:

`\begin{gathered} 3x-y=2 \\ \Rightarrow3(y-2)-y=2 \end{gathered}`

Solve for y:

`\begin{gathered} \Rightarrow3y-6-y=2 \\ \Rightarrow2y-6=2 \\ \Rightarrow2y=2+6 \\ \Rightarrow2y=8 \\ \Rightarrow y=(8)/(2) \\ \Rightarrow y=4 \end{gathered}`

Substitute y=4 into the expression of x to find its value:

`\begin{gathered} x=y-2 \\ \Rightarrow x=4-2 \\ \Rightarrow x=2 \end{gathered}`

Therefore, the solution to the given system is:

`\begin{gathered} x=2 \\ y=4 \end{gathered}`