SOLUTION: Solve by graphing. 3x + y = 5 -2x + 3y = 4

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Question 116998This question is from textbook
: Solve by graphing.
3x + y = 5
-2x + 3y = 4 This question is from textbook

Answer by jim_thompson5910(35256) 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%2By=5

-2x%2B3y=4





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%2By=5 Start with the given equation



1y=5-3x Subtract 3+x from both sides



1y=-3x%2B5 Rearrange the equation



y=%28-3x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-3x%2B5 Reduce



Now lets graph y=-3x%2B5 (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+-3x%2B5%29+ Graph of y=-3x%2B5




So let's solve for y on the second equation


-2x%2B3y=4 Start with the given equation



3y=4%2B2x Add 2+x to both sides



3y=%2B2x%2B4 Rearrange the equation



y=%28%2B2x%2B4%29%2F%283%29 Divide both sides by 3



y=%28%2B2%2F3%29x%2B%284%29%2F%283%29 Break up the fraction



y=%282%2F3%29x%2B4%2F3 Reduce





Now lets add the graph of y=%282%2F3%29x%2B4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B5%2C%282%2F3%29x%2B4%2F3%29+ Graph of y=-3x%2B5(red) and y=%282%2F3%29x%2B4%2F3(green)


From the graph, we can see that the two lines intersect at the point (1,2) (note: you might have to adjust the window to see the intersection)