SOLUTION: Solve the system of equations by graphing 2x+y=8 X+3y=9 What is the solution of the system of equations?

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Question 954446: Solve the system of equations by graphing
2x+y=8
X+3y=9
What is the solution of the system of equations?

Answer by MathLover1(20850) 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:


2x%2By=8

1x%2B3y=9





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


2x%2By=8 Start with the given equation



1y=8-2x Subtract 2+x from both sides



1y=-2x%2B8 Rearrange the equation



y=%28-2x%2B8%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%288%29%2F%281%29 Break up the fraction



y=-2x%2B8 Reduce



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




So let's solve for y on the second equation


1x%2B3y=9 Start with the given equation



3y=9-x Subtract +x from both sides



3y=-x%2B9 Rearrange the equation



y=%28-x%2B9%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%289%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B3 Reduce





Now lets add the graph of y=%28-1%2F3%29x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B8%2C%28-1%2F3%29x%2B3%29+ Graph of y=-2x%2B8(red) and y=%28-1%2F3%29x%2B3(green)


From the graph, we can see that the two lines intersect at the point (3,2) (note: you might have to adjust the window to see the intersection)