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

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) (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) (Show Source): You can put this solution on YOUR website!
Arrange both equations in slope-intercept form.
.
The first equation is:

Subtract x from both sides

Divide both sides by 4

.
The second equation is:

Subtract 2x from both sides

Divide both sides by -6

.
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.
.
The two equations will intersect the points will be the same.
.

Multiply both sides by 12 to remove the fractions

Subtract 4x from both sides

Subtract 9 from both sides

Divide both sides by -7

.
Graph

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