Solve the following system of equations graphically on the set of axes below.
y=x+8
y=−2x−4
To solve the system of equations graphically, we need to plot the graphs of both equations on the same set of axes.
First, let's plot the graph of y=x+8.
To do this, we need to find at least two points on this graph.
One way to find points on the graph is to choose values for x and then calculate the corresponding values for y using the equation.
Let's choose x=0.
When x=0, y=0+8=8.
So one point on the graph is (0,8).
Let's choose x=4.
When x=4, y=4+8=12.
So another point on the graph is (4,12).
Plotting these two points on the set of axes, we get the graph of y=x+8.
Next, let's plot the graph of y=−2x−4.
Again, we need to find at least two points on this graph to plot it.
Let's choose x=0.
When x=0, y=−2(0)−4=−4.
So one point on the graph is (0,−4).
Let's choose x=3.
When x=3, y=−2(3)−4=−6.
So another point on the graph is (3,−6).
Plotting these two points on the set of axes, we get the graph of y=−2x−4.
Now, we can see that the two graphs intersect at the point (2,10).
Therefore, the solution to the system of equations is x=2 and y=10.
Here is the graph of the two equations on the set of axes:
(Note: The axes and the graphs are not exactly to scale and are only for visual representation.)
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y|
| x+8
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| |
| |
|‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
| |
| -2x-4
| |
| |
| |
| |
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-10 -5 0 5 10 15 20 25 30 35 x