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

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Question 555378: 2x+y=5
3x-y+10

Solve by graphing
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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)