SOLUTION: Solve the system by graphing. Give the answer as a general ordered pair. (Simplify your answer completely.) x = y y − x = 0

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system by graphing. Give the answer as a general ordered pair. (Simplify your answer completely.) x = y y − x = 0       Log On


   

Question 1130556: Solve the system by graphing. Give the answer as a general ordered pair. (Simplify your answer completely.)
x = y
y − x = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x+=+y
y+-x+=+0
standard form
x+-y=0
-x+%2By=+0
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-y=0

-x%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-y=0 Start with the given equation



-y=0-x Subtract +x from both sides



-y=-x%2B0 Rearrange the equation



y=%28-x%2B0%29%2F%28-1%29 Divide both sides by -1



y=%28-1%2F-1%29x%2B%280%29%2F%28-1%29 Break up the fraction



y=x%2B0 Reduce



Now lets graph y=x%2B0 (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%2B0%29+ Graph of y=x%2B0




So let's solve for y on the second equation


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



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



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



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



y=%28%2B1%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=x%2B0 Reduce





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


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


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.