By graphing the given equations, we can determine the number of solutions to the system. These will be the points 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
As we can see the first equation is already in slope-intercept form. Let's highlight the m and b values.
y=3/2x ⇔ y=3/2x+ 0Let's rewrite the second equation in the system in slope-intercept form.
We can see that the slope m is 2, while the y-intercept b is 3.
Graphing the System
To graph these equations, we will start by plotting their y-intercepts. Then, we will use the slopes 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.
