SOLUTION: Graph the following system of equations using slope and Y-intercept. Determine the number of solutions for the system: 3x-5y=-5 and 6x-10y=-10

Algebra ->  Linear-equations -> SOLUTION: Graph the following system of equations using slope and Y-intercept. Determine the number of solutions for the system: 3x-5y=-5 and 6x-10y=-10      Log On


   

Question 691605: Graph the following system of equations using slope and Y-intercept. Determine the number of solutions for the system: 3x-5y=-5 and 6x-10y=-10
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-5y=-5

6x-10y=-10





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-5y=-5 Start with the given equation



-5y=-5-3x Subtract 3+x from both sides



-5y=-3x-5 Rearrange the equation



y=%28-3x-5%29%2F%28-5%29 Divide both sides by -5



y=%28-3%2F-5%29x%2B%28-5%29%2F%28-5%29 Break up the fraction



y=%283%2F5%29x%2B1 Reduce



Now lets graph y=%283%2F5%29x%2B1 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F5%29x%2B1%29+ Graph of y=%283%2F5%29x%2B1




So let's solve for y on the second equation


6x-10y=-10 Start with the given equation



-10y=-10-6x Subtract 6+x from both sides



-10y=-6x-10 Rearrange the equation



y=%28-6x-10%29%2F%28-10%29 Divide both sides by -10



y=%28-6%2F-10%29x%2B%28-10%29%2F%28-10%29 Break up the fraction



y=%283%2F5%29x%2B1 Reduce





Now lets add the graph of y=%283%2F5%29x%2B1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F5%29x%2B1%2C%283%2F5%29x%2B1%29+ Graph of y=%283%2F5%29x%2B1(red) and y=%283%2F5%29x%2B1(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3x-5y=-5
6x-10y=-10
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Multiply the top equation by 2:
6x -10y = -10
6x-10y = -10
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The 2 equations are really the same equation.
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Solution: All points of the form (x, (3/5)x +1)
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Cheers,
Stan H.
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