By graphing the given equations, we can determine the number of solutions to the system. 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. We will start by transforming the equations a little bit.
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
y=1.5x+1
y= 1.5x+ 1
1.5
(0, 1)
y=- 1.5x+5.5
y= - 1.5x+ 5.5
- 1.5
(0, 5.5)
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.
The solutions of the system of equations are the points at which the lines intersect. We can see that they intersect at exactly one point.
