Q 7 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

The solution to the linear equations is (0,2). 

Step 1. Given information

The given linear equations are

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

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.

$$\begin{gathered} y = x + 2 \\ \mathrm{Here} \mathrm{the} \mathrm{slope} \mathrm{is} m = 1 \\ \mathrm{And} \mathrm{the} \mathrm{y}-\mathrm{intercept} \mathrm{is} b = 2 \\ \mathrm{Again} \mathrm{Solve} \mathrm{the} \mathrm{second} \mathrm{equation} \mathrm{for} \mathrm{y}, \mathrm{and} \mathrm{find} \mathrm{the} \mathrm{slope} \mathrm{and} \mathrm{y}-\mathrm{intercept}. \\ y = - 2x + 2 \\ \mathrm{Here} \mathrm{the} \mathrm{slope} \mathrm{is} m = - 2 \\ \mathrm{And} \mathrm{the} \mathrm{y}-\mathrm{intercept} \mathrm{is} b = 2 \end{gathered}$$

Step 3. Graph obtained

Step 4. Checking the equation

$$\begin{gathered} \mathrm{Check}: \\ \mathrm{First} \mathrm{substitute} x = 0, \\ y = 2 \mathrm{Into} \mathrm{the} \mathrm{equation} \\ y = x + 2 . \\ y = x + 2 \\ 2=0+2 \\ 2=2 \\ \mathrm{This} \mathrm{is} \mathrm{true}. \\ \mathrm{Also} \mathrm{substitute} x = 0, \\ y = 2 \mathrm{into} \mathrm{the} \mathrm{equation} \\ y = - 2x + 2 \\ y = - 2x + 2 \\ 2=-2\left(0\right)+2 \\ 2=0+2 \\ 2=2 \\ \mathrm{This} \mathrm{is} \mathrm{true}. \\ \mathrm{The} \mathrm{solution} \mathrm{of} \mathrm{the} \mathrm{system} \mathrm{of} \mathrm{linear} \mathrm{equations} \mathrm{is} (0,2) \end{gathered}$$