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Question 804939: What is the point of intersection/whether the point is a solution for:
3x + y = 6
y = -3x + 2
Thanks. x
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! We have two linear equations:
L1: 3x + y = 6
L2: y = -3x + 2
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To solve them means to find the point or points of intersection, if any, between L1 and L2.
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Substitute (-3x + 2) (the value of y from L2) for y in L1:
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L1: 3x + y = 6
L1: 3x + (-3x + 2) = 6
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Now solve for x:
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3x - 3x + 2 = 6
2 = 6
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Answer:
The lines L1 and L2 do not intersect.
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Check the answer by converting L1 to slope-intercept form: y = mx + b
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L1: 3x + y = 6
y = -3x + 6
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Now we can see that L1 and L2 have the same slope (-3).
But L1 and L2 have different y-intercepts (6 for L1 and 2 for L2).
So L1 and L2 are parallel lines that never intersect.
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