SOLUTION: Solve each of the following systems by graphing. x-2y=8 3x-2y=12 I need to see this worked out. I know I need to convert to slope intercept form. So the first one I would d

Algebra ->  Graphs -> SOLUTION: Solve each of the following systems by graphing. x-2y=8 3x-2y=12 I need to see this worked out. I know I need to convert to slope intercept form. So the first one I would d      Log On


   

Question 111363: Solve each of the following systems by graphing.
x-2y=8
3x-2y=12
I need to see this worked out.
I know I need to convert to slope intercept form. So the first one I would do
x-2y=8
-x -x
-2y= -x+8
divide by -2 on both sides
y= x/2 + 4 SO I would start at the plot 0,4, then plot over 2 and up 1, so 2,5??
Then 3x-2y=12
-3x -3x
-2y= -3x + 12
divide by neg. 2 on both sides
y= 3/2x - 6
so the second set of points would be (0, -6), and (2,3)?
Is that correct, and then find the point they intercept which would be never?


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
Solved by pluggable solver: Solve the System of Equations by Graphing



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)