Q 6 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

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

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

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

This is true.

Similarly, substituting

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

In the equation

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

This is true.