Question

we are doing solving system of equations by substitution. can you please show me how to do this problem?2x-2y = -6x+6y=4

Answer 1

Starting from the given system of equations:

$\begin{gathered} 2x-2y=-6 \\ x+6y=4 \end{gathered}$

To solve a system by substitution, isolate one of the variables from one equation and substitute the expression for that variable on the other equation.

For instance, isolate x from the first equation:

$\begin{gathered} 2x-2y=-6 \\ \Rightarrow2x=2y-6 \\ \Rightarrow x=y-3 \end{gathered}$

Substitute x=y-3 in the second equation:

$\begin{gathered} x+6y=4 \\ \Rightarrow(y-3)+6y=4 \\ \Rightarrow7y-3=4 \\ \Rightarrow7y=4+3 \\ \Rightarrow7y=7 \\ \Rightarrow y=1 \end{gathered}$

Then, substitute back y=1 into the expression for x:

$\begin{gathered} x=y-3 \\ \Rightarrow x=(1)-3 \\ \Rightarrow x=-2 \end{gathered}$

Therefore, the solution to the system is:

$\begin{gathered} x=-2 \\ y=1 \end{gathered}$