SOLUTION: I have solved these but wanted someone check them. Is there any way you can solve these and graph them so that I can see what they look like compared to my graph since I am unsure

Algebra ->  Graphs -> SOLUTION: I have solved these but wanted someone check them. Is there any way you can solve these and graph them so that I can see what they look like compared to my graph since I am unsure       Log On


   

Question 88889: I have solved these but wanted someone check them. Is there any way you can solve these and graph them so that I can see what they look like compared to my graph since I am unsure how to graph on this site.
It says to solve graphically. State the colution.
#1 #2
2x-y=-6 -2x+y=-4
x+y=3 y-2x=3
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:


2x-y=-6

1x%2By=3





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-y=-6 Start with the given equation



-y=-6-2x Subtract 2+x from both sides



-y=-2x-6 Rearrange the equation



y=%28-2x-6%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%28-6%29%2F%28-1%29 Break up the fraction



y=2x%2B6 Reduce



Now lets graph y=2x%2B6 (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+2x%2B6%29+ Graph of y=2x%2B6




So let's solve for y on the second equation


1x%2By=3 Start with the given equation



1y=3-x Subtract +x from both sides



1y=-x%2B3 Rearrange the equation



y=%28-x%2B3%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%283%29%2F%281%29 Break up the fraction



y=-x%2B3 Reduce





Now lets add the graph of y=-x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B6%2C-x%2B3%29+ Graph of y=2x%2B6(red) and y=-x%2B3(green)


From the graph, we can see that the two lines intersect at the point (-1,4) (note: you might have to adjust the window to see the intersection)



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

#2
-2x%2By=-4
y-2x=3

-2x%2By=-4
-2x%2By=3 Rearrange the terms

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-2x%2By=-4

-2x%2By=3





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%2By=-4 Start with the given equation



1y=-4%2B2x Add 2+x to both sides



1y=%2B2x-4 Rearrange the equation



y=%28%2B2x-4%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%28-4%29%2F%281%29 Break up the fraction



y=2x-4 Reduce



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




So let's solve for y on the second equation


-2x%2By=3 Start with the given equation



1y=3%2B2x Add 2+x to both sides



1y=%2B2x%2B3 Rearrange the equation



y=%28%2B2x%2B3%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%283%29%2F%281%29 Break up the fraction



y=2x%2B3 Reduce





Now lets add the graph of y=2x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%2C2x%2B3%29+ Graph of y=2x-4(red) and y=2x%2B3(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.