SOLUTION: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION      Log On


   

Question 1130558: Solve the system by graphing. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION.)
y + 3x = 3
6x − 6 = −2y
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y+%2B+3x+=+3
6x+-6+=+-2y
standard form
3x+%2By=+3
6x+%2B2y+=+6

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



Start with the given system of equations:


3x%2By=3

6x%2B2y=6





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=3 Start with the given equation



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



1y=-3x%2B3 Rearrange the equation



y=%28-3x%2B3%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%283%29%2F%281%29 Break up the fraction



y=-3x%2B3 Reduce



Now lets graph y=-3x%2B3 (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%2B3%29+ Graph of y=-3x%2B3




So let's solve for y on the second equation


6x%2B2y=6 Start with the given equation



2y=6-6x Subtract 6+x from both sides



2y=-6x%2B6 Rearrange the equation



y=%28-6x%2B6%29%2F%282%29 Divide both sides by 2



y=%28-6%2F2%29x%2B%286%29%2F%282%29 Break up the fraction



y=-3x%2B3 Reduce





Now lets add the graph of y=-3x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B3%2C-3x%2B3%29+ Graph of y=-3x%2B3(red) and y=-3x%2B3(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.