SOLUTION: how do you find the graph of a system?

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Question 83689: how do you find the graph of a system?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets say you had the system of equations
x%2B2y=11
5x%2B3y=34

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



Start with the given system of equations:


1x%2B2y=11

5x%2B3y=34





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


1x%2B2y=11 Start with the given equation



2y=11-x Subtract +x from both sides



2y=-x%2B11 Rearrange the equation



y=%28-x%2B11%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%2811%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B11%2F2 Reduce



Now lets graph y=%28-1%2F2%29x%2B11%2F2 (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+%28-1%2F2%29x%2B11%2F2%29+ Graph of y=%28-1%2F2%29x%2B11%2F2




So let's solve for y on the second equation


5x%2B3y=34 Start with the given equation



3y=34-5x Subtract 5+x from both sides



3y=-5x%2B34 Rearrange the equation



y=%28-5x%2B34%29%2F%283%29 Divide both sides by 3



y=%28-5%2F3%29x%2B%2834%29%2F%283%29 Break up the fraction



y=%28-5%2F3%29x%2B34%2F3 Reduce





Now lets add the graph of y=%28-5%2F3%29x%2B34%2F3 to our first plot to get:


Graph of y=%28-1%2F2%29x%2B11%2F2(red) and y=%28-5%2F3%29x%2B34%2F3(green)


From the graph, we can see that the two lines intersect at the point (5,3) (note: you might have to adjust the window to see the intersection)