SOLUTION: Directions: on a coordinate system on a graph, graph each system of equations on the same set of axes. name the point of intersection. My two equations are y=3x+1 and y=x-1. How do

Algebra ->  Coordinate-system -> SOLUTION: Directions: on a coordinate system on a graph, graph each system of equations on the same set of axes. name the point of intersection. My two equations are y=3x+1 and y=x-1. How do      Log On


   

Question 122987: Directions: on a coordinate system on a graph, graph each system of equations on the same set of axes. name the point of intersection. My two equations are y=3x+1 and y=x-1. How do i graph them and where do i name the point of intersection?
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

y=3x%2B1 and y=x-1
in standard form:
-3x+%2B+y+=+1

and -x+%2B+y+=+-1
graph:
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-3x%2By=1

-x%2By=-1





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%2B3x Add 3+x to both sides



1y=%2B3x%2B1 Rearrange the equation



y=%28%2B3x%2B1%29%2F%281%29 Divide both sides by 1



y=%28%2B3%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


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



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



1y=%2Bx-1 Rearrange the equation



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



y=%28%2B1%2F1%29x%2B%28-1%29%2F%281%29 Break up the fraction



y=x-1 Reduce





Now lets add the graph of y=x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B1%2Cx-1%29+ Graph of y=3x%2B1(red) and y=x-1(green)


From the graph, we can see that the two lines intersect at the point (-1,-2) (note: you might have to adjust the window to see the intersection)