Solve the following system of equations graphically on the set of axes below.
y=-x+5
y=1/2x-4
since you have y = y
1/2 x - 4 = -x + 5
times 2
x - 8 = -2x + 10
3x = 18
x = 6, then y = -x+5 = -6+5 = -1
x = 6
y = -1
To solve the system of equations graphically, we will plot the equations on the set of axes and find the point of intersection, which represents the solution.
First, let's plot the first equation, y = -x + 5. To do this, we need two points. We can choose x = 0 and x = 5.
When x = 0, y = -0 + 5 = 5. So, the first point is (0, 5).
When x = 5, y = -5 + 5 = 0. So, the second point is (5, 0).
Plotting these points and drawing a line through them, we get the graph for the first equation:
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6 -|
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4 -| . (5, 0)
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2 -|
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0 -| . (0, 5)
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-1 0 1 2 3 4 5
Now, let's plot the second equation, y = 1/2x - 4. Again, we need two points. Choosing x = 0 and x = 8.
When x = 0, y = 1/2(0) - 4 = -4. So, the first point is (0, -4).
When x = 8, y = 1/2(8) - 4 = 0. So, the second point is (8, 0).
Plotting these points and drawing a line through them, we get the graph for the second equation:
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6 -|
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4 -| . (8, 0)
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2 -|
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0 -| . (0, -4)
|
-----------------------
-1 0 1 2 3 4 5 6 7 8
Now, we can find the point of intersection between these two lines. From the graph, it appears that the lines intersect at approximately (3, 2). Therefore, the solution to the system of equations is x = 3 and y = 2.
To solve the system of equations graphically, you will need to plot the lines represented by each equation on the set of axes provided. The point where the lines intersect is the solution to the system.
Let's start by plotting the first equation, y = -x + 5.
To do this, you can choose any two or more values for x and calculate the corresponding y-values. Here are a few x-values and their corresponding y-values to get you started:
When x = 0, y = -(0) + 5 = 5
When x = 1, y = -(1) + 5 = 4
When x = 2, y = -(2) + 5 = 3
Continue this process and plot the points on the coordinate plane. Once you have a few points, you can draw a line through them. Remember to extend the line to cover the entire graph.
Next, let's plot the second equation, y = (1/2)x - 4.
Similarly, choose a few x-values and calculate their corresponding y-values. Here are a few:
When x = 0, y = (1/2)(0) - 4 = -4
When x = 1, y = (1/2)(1) - 4 = -3.5
When x = 2, y = (1/2)(2) - 4 = -3
Plot these points on the coordinate plane and draw a line through them, extending it across the graph.
After plotting both lines, look for the point where the two lines intersect. This point represents the solution to the system of equations.
In this case, the lines intersect at the point (4, 1). Therefore, the solution to the system of equations is x = 4 and y = 1.
You can mark this point on the graph as the solution to the system of equations.