SOLUTION: Solve the system of equations by graphing 3x-y=3 and 4x+y=4

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Question 829756: Solve the system of equations by graphing 3x-y=3 and 4x+y=4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+3x-y=3
4x%2By=4
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Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-y=3

4x%2By=4





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


3x-y=3 Start with the given equation



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



-y=-3x%2B3 Rearrange the equation



y=%28-3x%2B3%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%283%29%2F%28-1%29 Break up the fraction



y=3x-3 Reduce



Now lets graph y=3x-3 (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+3x-3%29+ Graph of y=3x-3




So let's solve for y on the second equation


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



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



1y=-4x%2B4 Rearrange the equation



y=%28-4x%2B4%29%2F%281%29 Divide both sides by 1



y=%28-4%2F1%29x%2B%284%29%2F%281%29 Break up the fraction



y=-4x%2B4 Reduce





Now lets add the graph of y=-4x%2B4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-3%2C-4x%2B4%29+ Graph of y=3x-3(red) and y=-4x%2B4(green)


From the graph, we can see that the two lines intersect at the point (1,0) (note: you might have to adjust the window to see the intersection)





the two lines intersect at the point (1,+0+)