SOLUTION: Solve the following system by graphing: 3x-6y=9 x-2y=3 Equation 1 in slope intercept form: y-intercept as an ordered pair => x-intercept as an ordered pair =>

Algebra ->  Graphs -> SOLUTION: Solve the following system by graphing: 3x-6y=9 x-2y=3 Equation 1 in slope intercept form: y-intercept as an ordered pair => x-intercept as an ordered pair =>       Log On


   

Question 124951: Solve the following system by graphing:
3x-6y=9
x-2y=3
Equation 1 in slope intercept form:


y-intercept as an ordered pair =>
x-intercept as an ordered pair =>
Equation 2 in slope intercept form:


y-intercept as an ordered pair =>
x-intercept as an ordered pair =>

Graph of the system:


What is the solution for this system?

What type of system is this?
dependant
i need all the help i can get
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-6y=9
1x-2y=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-6y=9 Start with the given equation


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


-6y=-3x%2B9 Rearrange the equation


y=%28-3x%2B9%29%2F%28-6%29 Divide both sides by -6


y=%28-3%2F-6%29x%2B%289%29%2F%28-6%29 Break up the fraction


y=%281%2F2%29x-3%2F2 Reduce


Now lets graph y=%281%2F2%29x-3%2F2 (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+%281%2F2%29x-3%2F2%29+ Graph of y=%281%2F2%29x-3%2F2



So let's solve for y on the second equation

1x-2y=3 Start with the given equation


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


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


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


y=%28-1%2F-2%29x%2B%283%29%2F%28-2%29 Break up the fraction


y=%281%2F2%29x-3%2F2 Reduce



Now lets add the graph of y=%281%2F2%29x-3%2F2 to our first plot to get:

Graph of y=%281%2F2%29x-3%2F2(red) and y=%281%2F2%29x-3%2F2(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.