SOLUTION: Solve the system by graphing. 2x + y = 4 x + y = 3

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Question 126093: Solve the system by graphing.
2x + y = 4
x + y = 3
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=4
1x%2By=3




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=4 Start with the given equation


1y=4-2x Subtract 2+x from both sides


1y=-2x%2B4 Rearrange the equation


y=%28-2x%2B4%29%2F%281%29 Divide both sides by 1


y=%28-2%2F1%29x%2B%284%29%2F%281%29 Break up the fraction


y=-2x%2B4 Reduce


Now lets graph y=-2x%2B4 (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%2B4%29+ Graph of y=-2x%2B4



So let's solve for y on the second equation

1x%2By=3 Start with the given equation


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


1y=-x%2B3 Rearrange the equation


y=%28-x%2B3%29%2F%281%29 Divide both sides by 1


y=%28-1%2F1%29x%2B%283%29%2F%281%29 Break up the fraction


y=-x%2B3 Reduce



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

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B4%2C-x%2B3%29+ Graph of y=-2x%2B4(red) and y=-x%2B3(green)

From the graph, we can see that the two lines intersect at the point (1,2)