Q 8 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

The solution of the system of linear equations is (1,-1). 

Step 1. Given information

Two linear equations are

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

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

$$\begin{gathered} y=x-2 \\ \mathrm{Here} \mathrm{the} \mathrm{slope} \mathrm{is} m=1 \\ \mathrm{And} \mathrm{the} \mathrm{y}-\mathrm{intercept} \mathrm{is} b = -2 \end{gathered}$$

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

$$\begin{gathered} y = - 3x + 2 \\ \mathrm{Here} \mathrm{the} \mathrm{slope} \mathrm{is} m = - 3 \\ \mathrm{And} \mathrm{the} y-\mathrm{intercept} \mathrm{is} b = 2 \end{gathered}$$

Step 3. Graph obtained

Step 4. Checking the values

$$\begin{gathered} \mathbf{Check}\mathbf{ }\mathbf{:} \\ \mathrm{First} \mathrm{substitute} x = 1 , \\ y = - 1 \mathrm{into} \mathrm{the} \mathrm{equation} \\ y = x - 2 \\ y = x - 2 \\ -1=1-2 \\ -1=-1 \\ \mathrm{This} \mathrm{is} \mathrm{true}. \end{gathered}$$

$$\begin{gathered} \mathrm{Also} \mathrm{substitute} x = 1, \\ y = -1 \\ \mathrm{into} \mathrm{the} \mathrm{equation} y=-3x+2 \\ y=-3x+2 \\ -1=-3\left(1\right)+2 \\ -1=-3+2 \\ -1=-1 \\ \mathrm{This} \mathrm{is} \mathrm{true}. \end{gathered}$$