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

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Question 113306: Solve the system by graphing.
2x + y = 4
x + y = 3
Answer by MathLover1(20849) 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=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) (note: you might have to adjust the window to see the intersection)