Answer:
No solutions
Explanation:
Sorry to say, there are no solutions to this system of linear equations. A quick look at the attached graph will illustrate this conclusion. The two lines that go through the given points are parallel. They both have a slope of (1/3), with y-intercepts of 4 and -2.
Calculate the slopes of both lines:
Line A:
Point 1 (0,3)
Point 2 (3,4)
Rise = 4-3 = 1
Run = 3-0 = 3
Slope = Rise/Run = (1/3)
Line B:
Point 1 (0,-2)
Point 2 (3,-1)
Rise = -1-(-2) = 1
Run = 3-0 = 3
Slope = Rise/Run = (1/3)
Since the lines have the same slope, no more work is needed. They are parallel and will not intersect. Therefore, there are no solutions.
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If interested:
The y-intercept for each line can be found by using one of the points for each line in the equation y = mx + b, where m is the slope of (1/3) and b is the y-intercept.
Line 1: y = (1/3)x + b
3 = (1/3)*(0) + b for (0,3)
b = 3
Both lines have a slope of (1/3). They are parallel and will never meet, even though they have a lot in common.
Line 2: y = (1/3)x + b
-2 = (1/3)*(0) + b for (0,-2)
b = -2