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At what point do the lines 3x plus y equals 9 and 6x equals 4 - 2y intersect?
Wiki User
∙ 12y ago
Let's solve this by substitution. We're told:
3x + y = 9
6x = 4 - 2y
Let's start with the second equation, and solve for y:
6x = 4 - 2y
3x = 2 - y
2 - 3x = y
Now we can substitute it into the first equation, replacing all occurrences of y with 2 - 3x:
3x + (2 - 3x) = 9
2 = 9
Ah! That of course makes no sense, which tells us that the lines do not intersect at all, but are in fact parallel to each other. Let's confirm that by rearranging each of them into standard form:
3x + y = 9
y = 9 - 3x
y = -3x + 9
6x = 4 - 2y
y = 2 - 3x
y = -3x + 7
So there you have it. Those expressions describe two lines that have a slope of 3 and a y position that differs by 2.
Wiki User
∙ 12y ago
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x = 2 and y = 1 The lines intersect at the point (2, 1)
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What type of lines are y equals 2x and y equals 4x plus 2?
Those two statements are linear equations, not lines. If the equations are graphed, each one produces a straight line. The lines intersect at the point (-1, -2).
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Two straight lines that intersect.
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