SOLUTION: Graph each system of equations using the coordinate plane provided. Then determine whether the system has one solution, no solution, or infinitely many solutions. If the system has

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Graph each system of equations using the coordinate plane provided. Then determine whether the system has one solution, no solution, or infinitely many solutions. If the system has      Log On


   

Question 96826: Graph each system of equations using the coordinate plane provided. Then determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, name it.
2x-y=-3
6x-3y=-9
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:


2x-y=-3

6x-3y=-9





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


2x-y=-3 Start with the given equation



-y=-3-2x Subtract 2+x from both sides



-y=-2x-3 Rearrange the equation



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



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



y=2x%2B3 Reduce



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




So let's solve for y on the second equation


6x-3y=-9 Start with the given equation



-3y=-9-6x Subtract 6+x from both sides



-3y=-6x-9 Rearrange the equation



y=%28-6x-9%29%2F%28-3%29 Divide both sides by -3



y=%28-6%2F-3%29x%2B%28-9%29%2F%28-3%29 Break up the fraction



y=2x%2B3 Reduce





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B3%2C2x%2B3%29+ Graph of y=2x%2B3(red) and y=2x%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.