SOLUTION: If the system 3x+5=13 and ax+by=39 has more than one solution, determine the sum of a and b

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Question 1069276: If the system 3x+5=13 and ax+by=39 has more than one solution, determine the sum of a and b
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Multiple solutions means the equations are multiples of each other.
u%283x%2B5y%29=13u
3ux%2B5uy=13u
Compare to the second equation,
13u=39
u=3
So,
a=3u=3%283%29=9
b=5u=5%283%29=15

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If the system 3x+5=13 and ax+by=39 has more than one solution, determine the sum of a and b
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Both are linear equations, their graphs are straight lines.
If the graphs are parallel, there is no intersection, no solution.
If they are not parallel, there is 1 intersection, 1 solution.
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Only if they're dependent, ie, the same line twice, can there be > 1 solution.
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3x+5=13 and ax+by=39
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39/13 = 3
--> 3 times 3x+5y=13 (I think you meant 5y)
9x + 15y = 39
a+b = 24