By graphing the given equations, we can solve the system. If a solution exists, it will be the point at which the lines intersect. 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
y=1.5x+2
y=1.5x+ 2
1.5
(0, 2)
4.5x-3y=-9
y=1.5x+ 3
1.5
(0, 3)
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 are parallel. The lines have the same slope and different y-intercepts. They do not intersect, therefore the system has no solution.
