Question 248856
Arrange both equations in slope-intercept form.
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The first equation is:
{{{x+4y=3}}}
Subtract x from both sides
{{{4y = -x +3}}}
Divide both sides by 4
{{{y = -(1/4)x + 3/4}}}
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The second equation is:
{{{2x -6y = 8}}}
Subtract 2x from both sides
{{{-6y = -2x +8}}}
Divide both sides by -6
{{{y = (1/3)x - 4/3}}}
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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.
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{{{-(1/4)x + 3/4 = (1/3)x - 4/3}}}
Multiply both sides by 12 to remove the fractions
{{{-3x + 9 = 4x - 16}}}
Subtract 4x from both sides
{{{-7x + 9 = -16}}}
Subtract 9 from both sides
{{{-7x = -25}}}
Divide both sides by -7
{{{x = 25/7 = 3.5714}}}
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Graph
{{{
graph(500,500,-5,5,-5,5,-1/4*x+3/4, 1/3*x -4/3)
}}}