SOLUTION: solvw the system by graphing using the coordinate plane: 3x+y=1; x+y=5

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Question 84732: solvw the system by graphing using the coordinate plane: 3x+y=1; x+y=5
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:


3x%2By=1

1x%2By=5





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%2By=1 Start with the given equation



1y=1-3x Subtract 3+x from both sides



1y=-3x%2B1 Rearrange the equation



y=%28-3x%2B1%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%281%29%2F%281%29 Break up the fraction



y=-3x%2B1 Reduce



Now lets graph y=-3x%2B1 (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%2B1%29+ Graph of y=-3x%2B1




So let's solve for y on the second equation


1x%2By=5 Start with the given equation



1y=5-x Subtract +x from both sides



1y=-x%2B5 Rearrange the equation



y=%28-x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-x%2B5 Reduce





Now lets add the graph of y=-x%2B5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B1%2C-x%2B5%29+ Graph of y=-3x%2B1(red) and y=-x%2B5(green)


From the graph, we can see that the two lines intersect at the point (-2,7) (note: you might have to adjust the window to see the intersection)