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=- 2x-21
y=- 2x+( - 21)
- 2
(0, - 21)
y= x-7
y=1x+( - 7)
1
(0, -7)
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.
Notice that the slope indicated for the second equation is shown as 22. This is okay because slope is the rise divided by the run.
m=rise/run ⇒ m=1/1=2/2
We can see that the lines intersect at exactly one point.
However, we cannot identify the intersection point precisely. We can estimate that the intersection point is approximately (-4.6,-11.8). Now, let's check whether the point satisfies the equations.
The intersection point satisfies the first equation but it does not satisfy the second equation. The conclusion is that we cannot solve this system by graphing. Therefore, we will use the Substitution Method.
Substitution Method
Let's use the Substitution Method to solve the system of equations. Since the y-variables are already isolated, we will start with substituting x-7 for y into the first equation.
