Solve the system by graphing. Check your solution.
4x - y = 8
-2x - y = 2
To solve the system by graphing, we need to graph the equations on the same coordinate plane and find the intersection point.
First, let's rearrange the equations in slope-intercept form (y = mx + b):
Equation 1: 4x - y = 8
- Subtract 4x from both sides:
- y = -4x + 8
Equation 2: -2x - y = 2
- Subtract -2x from both sides:
- y = -2x + 2
Now we can graph these equations:
Equation 1 (blue):
- Plot the y-intercept at (0, 8) and use the slope, -4, to find additional points:
- When x = 2, y = -4(2) + 8 = 0 => Point (2, 0)
- When x = -2, y = -4(-2) + 8 = 16 => Point (-2, 16)
- Connect the points to graph the line.
Equation 2 (red):
- Plot the y-intercept at (0, 2) and use the slope, -2, to find additional points:
- When x = 1, y = -2(1) + 2 = 0 => Point (1, 0)
- When x = -1, y = -2(-1) + 2 = 4 => Point (-1, 4)
- Connect the points to graph the line.
The graph should look like this:
(5,20)
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-4 -2 0 2 4 6 8
The lines intersect at approximately (1.5, 6).
To check the solution, we substitute the point (1.5, 6) into both original equations:
Equation 1: 4(1.5) - 6 = 8
6 - 6 = 8
Equation 2: -2(1.5) - 6 = 2
-3 - 6 = 2
Both equations are not true, so (1.5, 6) is not the solution. It seems that there was an error in graphing. Let's try again:
The graph should look like this:
(5,20)
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-4 -2 0 2 4 6 8
The lines intersect at approximately (-2, -2).
To check the solution, we substitute the point (-2, -2) into both original equations:
Equation 1: 4(-2) - (-2) = 8
-8 + 2 = 8
Equation 2: -2(-2) - (-2) = 2
4 + 2 = 2
Both equations are not true, so (-2,-2) is not the solution.
It appears that there was an error in graphing again. Let's try once more:
The graph should look like this:
(5,20)
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-4 -2 0 2 4 6 8
The lines intersect at approximately (2, 0).
To check the solution, we substitute the point (2, 0) into both original equations:
Equation 1: 4(2) - 0 = 8
8 = 8
Equation 2: -2(2) - 0 = 2
-4 = 2
Both equations are not true, so (2, 0) is not the solution.
From our graph, it seems that there is no intersection point between the lines. Thus, there is no solution to the system of equations.