You will need two points for each equation to draw their graphs.
(- 1,3)
Practice makes perfect
By graphing the given equations, we can determine the solution to the system. This will be the point at which the lines intersect. To do this, we will need the equations to be written in slope-intercept form. This will to help us to identify the slope m and y-intercept b of each line.
Write in Slope-Intercept Form
Let's rewrite each of the equations in the system in slope-intercept form, highlighting the values of m and b.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
2x-y=- 5
y=2x+ 5
2
5
- 2x-y=- 1
y=- 2x+ 1
- 2
1
Graphing the System
To graph these equations, we will start by plotting their y-intercepts. Then, we will use the slope to determine another point that satisfies each equation, and finally connect the points with a line.
We can see that the lines intersect at exactly one point.
It appears that the lines intersect at (- 1, 3). This is the solution to the system.
Checking Our Solution
To check our answer, we will substitute the solution into the given equations. If the substitutions result in true statements, then we know that we have found the correct answer.
