Question

Solve the system of equations below.x + y = 5-4– 2y = -8Which point on the graph below is the solution to the system of linear equations?

Answer 1

$\begin{gathered} x+y=5 \\ -4x-2y=-8 \end{gathered}$

we solve the system replacing an equation on the other

We solve y from the first equation

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

now we can replace the value of y on the second equation

$\begin{gathered} -4x-2y=-8 \\ -4x-2(5-x)=-8 \end{gathered}$

Simplify

$\begin{gathered} -4x-10+2x=-8 \\ -2x-10=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-\frac{2}{2} \\ \\ x=-1 \end{gathered}$

the first coordinate of the solution point is x=-1, now we can replace x on any equation to find y

we will use first equation solved for y

$\begin{gathered} y=5-x \\ y=5-(-1) \\ y=6 \end{gathered}$

the second coordinate is 6

now the solution point is

$(-1,6)$

and the correct line point is W