SOLUTION: Help me understand how to Solve a Linear System by Graphing. y=x+2 y=-x+6

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Question 134399: Help me understand how to Solve a Linear System by Graphing.
y=x+2
y=-x+6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=x%2B2
y=-x%2B6
written in standard form:
-x+%2B+y=2
x+%2B+y=6
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-x%2By=2

1x%2By=6





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


-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 graph y=x%2B2 (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%2B2%29+ Graph of y=x%2B2




So let's solve for y on the second equation


1x%2By=6 Start with the given equation



1y=6-x Subtract +x from both sides



1y=-x%2B6 Rearrange the equation



y=%28-x%2B6%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%286%29%2F%281%29 Break up the fraction



y=-x%2B6 Reduce





Now lets add the graph of y=-x%2B6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2%2C-x%2B6%29+ Graph of y=x%2B2(red) and y=-x%2B6(green)


From the graph, we can see that the two lines intersect at the point (2,4) (note: you might have to adjust the window to see the intersection)