SOLUTION: Solve the following system by graphing: x-2y=8 3x-2y=12 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: x-2y=8 3x-2y=12 Equation 1 in slope intercept form: y-intercept as an ordered pair => x-intercept as an ordered pair =>       Log On


   

Question 124950: Solve the following system by graphing:
x-2y=8
3x-2y=12
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?

PLEASE HELPL ME I AM SOO CONFUSED!!!!!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

1x-2y=8
3x-2y=12




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

1x-2y=8 Start with the given equation


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


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


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


y=%28-1%2F-2%29x%2B%288%29%2F%28-2%29 Break up the fraction


y=%281%2F2%29x-4 Reduce


Now lets graph y=%281%2F2%29x-4 (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-4%29+ Graph of y=%281%2F2%29x-4



So let's solve for y on the second equation

3x-2y=12 Start with the given equation


-2y=12-3x Subtract 3+x from both sides


-2y=-3x%2B12 Rearrange the equation


y=%28-3x%2B12%29%2F%28-2%29 Divide both sides by -2


y=%28-3%2F-2%29x%2B%2812%29%2F%28-2%29 Break up the fraction


y=%283%2F2%29x-6 Reduce



Now lets add the graph of y=%283%2F2%29x-6 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-4%2C%283%2F2%29x-6%29+ Graph of y=%281%2F2%29x-4(red) and y=%283%2F2%29x-6(green)

From the graph, we can see that the two lines intersect at the point (2,-3) (note: you might have to adjust the window to see the intersection)