SOLUTION: Please help me solve this equation by graphing - 5X + Y = -9 X + 3y = 21

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Question 988926: Please help me solve this equation by graphing - 5X + Y = -9
X + 3y = 21

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
-5x+%2B+y=+-9
x%2B+3y+=+21
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Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-5x%2By=-9

1x%2B3y=21





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


-5x%2By=-9 Start with the given equation



1y=-9%2B5x Add 5+x to both sides



1y=%2B5x-9 Rearrange the equation



y=%28%2B5x-9%29%2F%281%29 Divide both sides by 1



y=%28%2B5%2F1%29x%2B%28-9%29%2F%281%29 Break up the fraction



y=5x-9 Reduce



Now lets graph y=5x-9 (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+5x-9%29+ Graph of y=5x-9




So let's solve for y on the second equation


1x%2B3y=21 Start with the given equation



3y=21-x Subtract +x from both sides



3y=-x%2B21 Rearrange the equation



y=%28-x%2B21%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%2821%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B7 Reduce





Now lets add the graph of y=%28-1%2F3%29x%2B7 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+5x-9%2C%28-1%2F3%29x%2B7%29+ Graph of y=5x-9(red) and y=%28-1%2F3%29x%2B7(green)


From the graph, we can see that the two lines intersect at the point (3,6) (note: you might have to adjust the window to see the intersection)