Question 189764
There are actually (4) possibilities when given 2 equations
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(1) They could actually be the SAME line
{{{3x + 2y = 8}}}
{{{6x + 4y = 16}}}
These are the same line because one is an
exact multiple of the other
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(2) They can be parallel lines
If the slope of one = the slope of the other
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(3) Perpendicular lines
If the slope of one  = the negative reciprocal
of the slope of the other
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(4) Two different lines, neither parallel nor perpendicular
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{{{3x + 5y = 3}}}
{{{5x + 3y = 4}}}
These need to be put in the slope-intercept form
which is: {{{y = mx + b}}} (m is the slope)
{{{3x + 5y = 3}}}
Subtract {{{3x}}} from both sides
{{{5y = -3x + 3}}}
Divide both sides by {{{5}}}
{{{y = -(3/5)x + 3}}}
Notice that {{{m = -3/5}}}
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{{{5x + 3y = 4}}}
Subtract {{{5x}}} from both sides
{{{3y = -5x + 4}}}
Divide both sides by {{{3}}}
{{{y = -(5/3)x + 4}}}
Notice {{{m = -5/3}}}
If this slope was 5/3, it would be perpendicular
to the other line.
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These two lines are neither the same line, parallel, or
perpendicular. I'll plot them:
{{{ graph( 500, 500, -10, 10, -10, 10, -(3/5)x + 3, -(5/3)x + 4) }}}