SOLUTION: I thought I would understand the graphing thing, apparently I don't. Any cahnce I can get some help? I have to graph 3x+2y=8 6x+4y=16 Please and Thank You=)

Algebra ->  Graphs -> SOLUTION: I thought I would understand the graphing thing, apparently I don't. Any cahnce I can get some help? I have to graph 3x+2y=8 6x+4y=16 Please and Thank You=)      Log On


   

Question 130091This question is from textbook algebra
: I thought I would understand the graphing thing, apparently I don't. Any cahnce I can get some help?
I have to graph
3x+2y=8
6x+4y=16
Please and Thank You=) This question is from textbook algebra

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%2B2y=8
6x%2B4y=16




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%2B2y=8 Start with the given equation


2y=8-3x Subtract 3+x from both sides


2y=-3x%2B8 Rearrange the equation


y=%28-3x%2B8%29%2F%282%29 Divide both sides by 2


y=%28-3%2F2%29x%2B%288%29%2F%282%29 Break up the fraction


y=%28-3%2F2%29x%2B4 Reduce


Now lets graph y=%28-3%2F2%29x%2B4





Looking at y=-%283%2F2%29x%2B4 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-3%2F2 and the y-intercept is b=4


Since b=4 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -3%2F2, this means:

rise%2Frun=-3%2F2


which shows us that the rise is -3 and the run is 2. This means that to go from point to point, we can go down 3 and over 2



So starting at , go down 3 units


and to the right 2 units to get to the next point



Now draw a line through these points to graph y=-%283%2F2%29x%2B4

So this is the graph of y=-%283%2F2%29x%2B4 through the points and





So let's solve for y on the second equation

6x%2B4y=16 Start with the given equation


4y=16-6x Subtract 6+x from both sides


4y=-6x%2B16 Rearrange the equation


y=%28-6x%2B16%29%2F%284%29 Divide both sides by 4


y=%28-6%2F4%29x%2B%2816%29%2F%284%29 Break up the fraction


y=%28-3%2F2%29x%2B4 Reduce



Now lets add the graph of y=%28-3%2F2%29x%2B4 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F2%29x%2B4%2C%28-3%2F2%29x%2B4%29+ Graph of y=%28-3%2F2%29x%2B4(red) and y=%28-3%2F2%29x%2B4(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.