By graphing the given equations, we can determine the number of solutions to the system. This 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
x+8/3y=12
y=-3/8x+ 9/2
-3/8
(0, 9/2)
1/2x+4/3y=6
y=-3/8x+ 9/2
-3/8
(0, 9/2)
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 from our graph that these lines are the same. Therefore, every point on the line is a solution to the system, and there are infinitely many solutions.
