SOLUTION: Solve the system by graphing. 3x + y = –1 9x + 3y = –3

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Question 126106:
Solve the system by graphing.
3x + y = –1 9x + 3y = –3
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

3x%2By=-1
9x%2B3y=-3




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-1 Rearrange the equation


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


y=%28-3%2F1%29x%2B%28-1%29%2F%281%29 Break up the fraction


y=-3x-1 Reduce


Now lets graph y=-3x-1 (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-1%29+ Graph of y=-3x-1



So let's solve for y on the second equation

9x%2B3y=-3 Start with the given equation


3y=-3-9x Subtract 9+x from both sides


3y=-9x-3 Rearrange the equation


y=%28-9x-3%29%2F%283%29 Divide both sides by 3


y=%28-9%2F3%29x%2B%28-3%29%2F%283%29 Break up the fraction


y=-3x-1 Reduce



Now lets add the graph of y=-3x-1 to our first plot to get:

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

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
3X+Y=-1 OR Y=-3X-1 (RED LINE)
9X+3Y=-3 OR 3Y=-9X-3 (GREEN LINE)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-3x+-1%2C+-9x+-3%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -3x -1 and -9x -3).
ANSWER (-1/3,0)