SOLUTION: Solve the following systems by graphing: 2x-3y = 12 -2x+y -8 I finished the problem and then checked my answer in the back of the book. I got the first one correct but canno

Algebra ->  Graphs -> SOLUTION: Solve the following systems by graphing: 2x-3y = 12 -2x+y -8 I finished the problem and then checked my answer in the back of the book. I got the first one correct but canno      Log On


   

Question 106122This question is from textbook Elementary and Intermediate Algebra
: Solve the following systems by graphing:
2x-3y = 12
-2x+y -8
I finished the problem and then checked my answer in the back of the book. I got the first one correct but cannot figure out the second part.

This question is from textbook Elementary and Intermediate Algebra

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.
2x-3y+=+12
2.
-2x%2By+-8
=> -2x%2By+=+8
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-3y=12

-2x%2By=8





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


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



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



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



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



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



y=%282%2F3%29x-4 Reduce



Now lets graph y=%282%2F3%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+%282%2F3%29x-4%29+ Graph of y=%282%2F3%29x-4




So let's solve for y on the second equation


-2x%2By=8 Start with the given equation



1y=8%2B2x Add 2+x to both sides



1y=%2B2x%2B8 Rearrange the equation



y=%28%2B2x%2B8%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%288%29%2F%281%29 Break up the fraction



y=2x%2B8 Reduce





Now lets add the graph of y=2x%2B8 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-4%2C2x%2B8%29+ Graph of y=%282%2F3%29x-4(red) and y=2x%2B8(green)


From the graph, we can see that the two lines intersect at the point (-9,-10) (note: you might have to adjust the window to see the intersection)