SOLUTION: I need to solve tis by graphing and have done this ten times and still can not find the points to graph. 3x-2y=6 3x+2y=6 Could somebody please help me figure out how to graph

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I need to solve tis by graphing and have done this ten times and still can not find the points to graph. 3x-2y=6 3x+2y=6 Could somebody please help me figure out how to graph       Log On


   

Question 173156: I need to solve tis by graphing and have done this ten times and still can not find the points to graph.
3x-2y=6
3x+2y=6
Could somebody please help me figure out how to graph this? Thank you in advance. Judy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:


system%283x-2y=6%2C3x%2B2y=6%29



Let's graph the first equation:


3x-2y=6 Start with the first equation.


-2y=6-3x Subtract 3x from both sides.


-2y=-3x%2B6 Rearrange the terms.


y=%28-3x%2B6%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=%28%28-3%29%2F%28-2%29%29x%2B%286%29%2F%28-2%29 Break up the fraction.


y=%283%2F2%29x-3 Reduce.


Now let's graph the equation:




Looking at y=%283%2F2%29x-3 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=-3


Since b=-3 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 up 3 and over 2



So starting at , go up 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-3

So this is the graph of y=%283%2F2%29x-3 through the points and


-------------------------------------------------------------------


Now let's graph the second equation:


3x%2B2y=6 Start with the second equation.


2y=6-3x Subtract 3x from both sides.


2y=-3x%2B6 Rearrange the terms.


y=%28-3x%2B6%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%28-3%29%2F%282%29%29x%2B%286%29%2F%282%29 Break up the fraction.


y=-%283%2F2%29x%2B3 Reduce.




Looking at y=-%283%2F2%29x%2B3 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=3


Since b=3 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%2B3

So this is the graph of y=-%283%2F2%29x%2B3 through the points and


-------------------------------------------------------------------


Now let's graph the two equations together:


Graph of y=%283%2F2%29x-3 (red). Graph of y=-%283%2F2%29x%2B3 (green)


From the graph, we can see that the two lines intersect at the point .


So the solution to the system of equations is .


This tells us that the system of equations is consistent and independent.