Chapter 2.1, Problem 18E

To determine

To find: of the system of given equations by graphing.

Answer to Problem 18E

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

Explanation of Solution

Given information:

  $\begin{array}{l}y=x-2\mathrm{...}\left(1\right)\\ x-2y=4\mathrm{...}\left(2\right)\end{array}$

Calculation:

On comparing the equation (1) with slope intercept formula, we get the value of slope as $1$ and y-intercept as $-2$ .

Convert equation (2) into slope intercept form to evaluate the value of slope and y-intercept as follows:

  $\begin{array}{c}x-2y=4\\ -2y=-x+4\\ y=\frac{-1}{-2}x+\frac{4}{-2}\\ y=\frac{1}{2}x-2\end{array}$

Thus, the value of slope is $\frac{1}{2}$ and y-intercept is $-2$ .

Since, both the slopes have different values and the lines are not perpendicular to each other. So, they will intersect at some point.

Put different values of x in equation (1) to get different values of y, and then graph the line.

Similarly, put different values of x in equation (2) to get different values of y, and then graph the line as follows:

  

So, the point of intersection is $\left(0,-2\right)$ . That is, the value of x and y is 0 and $-2$ respectively.