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

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Question 85702: Solve the system by graphing.
x + y = 4
–x + y = 2
Found 2 solutions by jim_thompson5910, checkley75:
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:


1x%2By=4

-x%2By=2





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


1x%2By=4 Start with the given equation



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



1y=-x%2B4 Rearrange the equation



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



y=%28-1%2F1%29x%2B%284%29%2F%281%29 Break up the fraction



y=-x%2B4 Reduce



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




So let's solve for y on the second equation


-x%2By=2 Start with the given equation



1y=2%2Bx Add +x to both sides



1y=%2Bx%2B2 Rearrange the equation



y=%28%2Bx%2B2%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%282%29%2F%281%29 Break up the fraction



y=x%2B2 Reduce





Now lets add the graph of y=x%2B2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%2Cx%2B2%29+ Graph of y=-x%2B4(red) and y=x%2B2(green)


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

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=4, Y=-X+4 (RED LINE)
-X+Y=2, Y=X+2 (GREEN LINE)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+-x+%2B4%2C+y+=+x+%2B2%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = -x +4 and y = x +2).
SOLUTION IS (1,3).