SOLUTION: without graphing determine the number of solutions of the following system of equations: 4x-10y=-5 and 2x-5y=0

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Question 557217: without graphing determine the number of solutions of the following system of equations: 4x-10y=-5 and 2x-5y=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +4x+-+10y+=+-5+
(2) +2x+-+5y+=+0+
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They are straight lines, so they must either:
(1) intersect at 1 point ( different slopes )
(2) Not intersect ( same slope )
(3) They are actually the same line
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If I divide both sides of (1) by 2,
I get
(1) +2x+-+5y+=+-%285%2F2%29+
(1) +5y+=+2x+%2B+%285%2F2%29+
(1) +y+=+%282%2F5%29%2Ax+%2B+%281%2F2%29+
and
(2) +2x+-+5y+=+0+
(2) +5y+=+2x+
(2) +y+=+%282%2F5%29%2Ax+
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The lines have the same slope, and they are not
the same line, so they must be parallel.
Parallel lines have no solution.