SOLUTION: Determine where the two lines x+4y=3 and 2x-6y=8 intersect?

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Question 248856: Determine where the two lines x+4y=3 and 2x-6y=8 intersect?
Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine where the two lines
x+4y=3 and
2x-6y=8 intersect?
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Multiply thru the 1st equation by 2:
2x + 8y = 6
2x - 6y = 8
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Subtract the 2nd Eq from the 1st and solve for "y":
14y = -2
y = -1/7
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Substitute in x + 4y = 3 and solve for "x":
x + 4(-1/7) = 3
x - 4/7 = 21/7
x = 25/7
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Cheers,
Stan H.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Arrange both equations in slope-intercept form.
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The first equation is:
x%2B4y=3
Subtract x from both sides
4y+=+-x+%2B3
Divide both sides by 4
y+=+-%281%2F4%29x+%2B+3%2F4
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The second equation is:
2x+-6y+=+8
Subtract 2x from both sides
-6y+=+-2x+%2B8
Divide both sides by -6
y+=+%281%2F3%29x+-+4%2F3
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By inspection, we know the two lines are not parallel because they do not have the same slope. So they cannot be the same line. We also can tell they are not perpendicular.
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The two equations will intersect the points will be the same.
.
-%281%2F4%29x+%2B+3%2F4+=+%281%2F3%29x+-+4%2F3
Multiply both sides by 12 to remove the fractions
-3x+%2B+9+=+4x+-+16
Subtract 4x from both sides
-7x+%2B+9+=+-16
Subtract 9 from both sides
-7x+=+-25
Divide both sides by -7
x+=+25%2F7+=+3.5714
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Graph
%0D%0Agraph%28500%2C500%2C-5%2C5%2C-5%2C5%2C-1%2F4%2Ax%2B3%2F4%2C+1%2F3%2Ax+-4%2F3%29%0D%0A