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Question 1093164: Are the two equations -6+y=2x and 2y-4x12 dependent?
Found 2 solutions by ikleyn, addingup:
Answer by ikleyn(52781)   (Show Source):
Answer by addingup(3677)  (Show Source):
You can put this solution on YOUR website! -6+y=2x
y = 2x-6
y = 2(0)-6 = (0, -6) we now have one ordered pair, one dot in the graph.
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-6+y = 2x
2x = -6+y
x = 1/2(-6+y)
x = 1/2(-6+0) = (-3, 0) now we have a second dot in the graph, we can draw a line
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2y-4x=12 I think you're missing a sign between 4x and 12, is it = ?
I'll assume it is:
2y-4x = 12
2y = 4x + 12
y = 2x + 6
y = 2(0)+6, (0, 6)
2y-4x = 12
-4x = 12-2y
x = -3-1/2y
x = -3-(1/2(0)), (-3, 0)
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So, from the two equations we have two ordered pairs. What do you notice about these two sets of ordered pairs?
The first equation: (0,-6),(-3,0)
The second equation: (0,-6),(-3,0)
We got the same set of ordered pairs.
How do you know if a system of equations is dependent? When you graph the equations, both equations represent the same line.
Make a graph of the two sets of ordered pairs. Do they represent the same line?
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