Question

Section 5.2-8. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-3x+y = 12x-y = 2

Answer 1

To solve the system:

$\begin{gathered} -3x+y=1 \\ 2x-y=2 \end{gathered}$

we solve the second equation for y:

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

and substitute the value of y in the first equation and solve for x:

$\begin{gathered} -3x+2x-2=1 \\ -x=3 \\ x=-3 \end{gathered}$

Now we plug the value of x in the expression for y:

$\begin{gathered} y=2(-3)-2 \\ y=-6-2 \\ y=-8 \end{gathered}$

Therefore x=-3 and y=-8