SOLUTION: Find the solution to each system of equations by graphing Y=-x+4 Y=3x

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Question 1151013: Find the solution to each system of equations by graphing
Y=-x+4
Y=3x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=-x%2B4
y=3x
-------------------------
x%2By=4
-3x%2By=0

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=4

-3x%2By=0





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


-3x%2By=0 Start with the given equation



1y=0%2B3x Add 3+x to both sides



1y=%2B3x%2B0 Rearrange the equation



y=%28%2B3x%2B0%29%2F%281%29 Divide both sides by 1



y=%28%2B3%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=3x%2B0 Reduce





Now lets add the graph of y=3x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%2C3x%2B0%29+ Graph of y=-x%2B4(red) and y=3x%2B0(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)