SOLUTION: Solve by graphing. 2x + y = 5 3x - y = 10

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Question 117001This question is from textbook
: Solve by graphing.
2x + y = 5
3x - y = 10 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:


2x%2By=5

3x-y=10





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=5 Start with the given equation



1y=5-2x Subtract 2+x from both sides



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



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



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



y=-2x%2B5 Reduce



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




So let's solve for y on the second equation


3x-y=10 Start with the given equation



-y=10-3x Subtract 3+x from both sides



-y=-3x%2B10 Rearrange the equation



y=%28-3x%2B10%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%2810%29%2F%28-1%29 Break up the fraction



y=3x-10 Reduce





Now lets add the graph of y=3x-10 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B5%2C3x-10%29+ Graph of y=-2x%2B5(red) and y=3x-10(green)


From the graph, we can see that the two lines intersect at the point (3,-1) (note: you might have to adjust the window to see the intersection)