Does either of the equations have an isolated variable in it?
(3,2.5)
Practice makes perfect
In this system of equations,
neither of the equations has an isolated variable. Therefore, we can determine the solutions by graphing the given equations. To do this, we will need the equations to be in slope-intercept form to help us identify the slope m and y-intercept b.
Write in Slope-Intercept Form
Let's rewrite each of the equations in the system in slope-intercept form, highlighting the m and b values.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
0.5x+y=4
y=- 0.5x+4 ⇕ y= - 1/2x+ 4
- 1/2
(0, 4)
0.5x-y=- 1
y=0.5x+1 ⇕ y= 1/2x+ 1
1/2
(0, 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 connect the points with a line.
We can see that the lines intersect at exactly one point.
