Question

In the following exercises, solve the following systems of equations by graphing.

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

Short answer

The solution of the system of linear equations is (-2,0).

Step-by-step solution

Step 1. Given information 

Two linear equations are

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

Step 2. Solving equations for the intersection points

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y.

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

here the slope is $m=1$

and th y-intercept is$b=2$

Again find the slope and y-intercept by solving the Second equation for y.

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

here the slope is $m=-2$

and y intercept is$b=-4$

Step 3. Graph obtained 

The solution of the system of linear equations is (-2,0).

Step 4. Check 

Check:

First substitute

$$\begin{gathered} x=-2 \\ y=0 \end{gathered}$$

in the equation

localid="1644947528066" $$\begin{gathered} -x+y=2 \\ -(-2)+0=2 \\ 2=2 \end{gathered}$$

This is true.

Similarly, substituting

localid="1644947547170" $$\begin{gathered} x=-2 \\ y=0 \end{gathered}$$

In the equation

localid="1644947540734" $$\begin{gathered} 2x+y=-4 \\ 2(-2)=0=-4 \\ -4=-4 \end{gathered}$$

This is true.