SOLUTION: does 3x+7y=8 and 21y=-9x+24 have one solution, no solution or infinitly many solutions

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Question 750418: does 3x+7y=8 and 21y=-9x+24 have one solution, no solution or infinitly many solutions
Found 2 solutions by MathLover1, tommyt3rd:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B7y=8 and
21y=-9x%2B24
____________________solve the system
3x%2B7y=8
9x%2B21y=24


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



Start with the given system of equations:


3x%2B7y=8

9x%2B21y=24





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%2B7y=8 Start with the given equation



7y=8-3x Subtract 3+x from both sides



7y=-3x%2B8 Rearrange the equation



y=%28-3x%2B8%29%2F%287%29 Divide both sides by 7



y=%28-3%2F7%29x%2B%288%29%2F%287%29 Break up the fraction



y=%28-3%2F7%29x%2B8%2F7 Reduce



Now lets graph y=%28-3%2F7%29x%2B8%2F7 (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+%28-3%2F7%29x%2B8%2F7%29+ Graph of y=%28-3%2F7%29x%2B8%2F7




So let's solve for y on the second equation


9x%2B21y=24 Start with the given equation



21y=24-9x Subtract 9+x from both sides



21y=-9x%2B24 Rearrange the equation



y=%28-9x%2B24%29%2F%2821%29 Divide both sides by 21



y=%28-9%2F21%29x%2B%2824%29%2F%2821%29 Break up the fraction



y=%28-3%2F7%29x%2B8%2F7 Reduce





Now lets add the graph of y=%28-3%2F7%29x%2B8%2F7 to our first plot to get:


Graph of y=%28-3%2F7%29x%2B8%2F7(red) and y=%28-3%2F7%29x%2B8%2F7(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 tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
21y=-9x+24 can be rewritten as 9x+21y=24 and then 3x+7y=8. So it has the same graph (solution) as the first equation. So...many solutions

:)