SOLUTION: Hello, A while back, I was looking for help in figuring out the graphs below. I haven't gotten an answer yet. Graph the following: a) x+y=-3 2x-3y=4 b) x-y=3 2x+

Algebra ->  Graphs -> SOLUTION: Hello, A while back, I was looking for help in figuring out the graphs below. I haven't gotten an answer yet. Graph the following: a) x+y=-3 2x-3y=4 b) x-y=3 2x+      Log On


   

Question 904954: Hello,
A while back, I was looking for help in figuring out the graphs below. I haven't gotten an answer yet.
Graph the following:
a) x+y=-3
2x-3y=4
b) x-y=3
2x+3y=-4
c) x+y=3
2x+3y=4
d) x+y=-3
2x-3y=-4
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Not following the rules is a good reason not to get an answer
Here are the website rules.
Three simple Website rules
a) Limit 5 problems within 24 hours
b) No similar problems
c) Submit one problem one at a time once
Two is not one.
No similar problems
Similar means they are the same type problem but differ by the numbers or addition vs subtraction.
So you broke two of the three rules in one try. Too many problems and they are similar.
This suggests to us that you are not trying to learn but just want us to do your homework for you.
About 50% of the problems get answered.

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

a)
x%2By=-3
2x-3y=4
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=-3

2x-3y=4





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%2By=-3 Start with the given equation



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



1y=-x-3 Rearrange the equation



y=%28-x-3%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%28-3%29%2F%281%29 Break up the fraction



y=-x-3 Reduce



Now lets graph y=-x-3 (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+-x-3%29+ Graph of y=-x-3




So let's solve for y on the second equation


2x-3y=4 Start with the given equation



-3y=4-2x Subtract 2+x from both sides



-3y=-2x%2B4 Rearrange the equation



y=%28-2x%2B4%29%2F%28-3%29 Divide both sides by -3



y=%28-2%2F-3%29x%2B%284%29%2F%28-3%29 Break up the fraction



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





Now lets add the graph of y=%282%2F3%29x-4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x-3%2C%282%2F3%29x-4%2F3%29+ Graph of y=-x-3(red) and y=%282%2F3%29x-4%2F3(green)


From the graph, we can see that the two lines intersect at the point (-1,-2) (note: you might have to adjust the window to see the intersection)


b)
x-y=3
2x%2B3y=-4
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-y=3

2x%2B3y=-4





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-y=3 Start with the given equation



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



-y=-x%2B3 Rearrange the equation



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



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



y=x-3 Reduce



Now lets graph y=x-3 (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+x-3%29+ Graph of y=x-3




So let's solve for y on the second equation


2x%2B3y=-4 Start with the given equation



3y=-4-2x Subtract 2+x from both sides



3y=-2x-4 Rearrange the equation



y=%28-2x-4%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%28-4%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x-4%2F3 Reduce





Now lets add the graph of y=%28-2%2F3%29x-4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-3%2C%28-2%2F3%29x-4%2F3%29+ Graph of y=x-3(red) and y=%28-2%2F3%29x-4%2F3(green)


From the graph, we can see that the two lines intersect at the point (1,-2) (note: you might have to adjust the window to see the intersection)

c)
x%2By=3
2x%2B3y=4
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=3

2x%2B3y=4





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%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 graph y=-x%2B3 (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+-x%2B3%29+ Graph of y=-x%2B3




So let's solve for y on the second equation


2x%2B3y=4 Start with the given equation



3y=4-2x Subtract 2+x from both sides



3y=-2x%2B4 Rearrange the equation



y=%28-2x%2B4%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%284%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x%2B4%2F3 Reduce





Now lets add the graph of y=%28-2%2F3%29x%2B4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B3%2C%28-2%2F3%29x%2B4%2F3%29+ Graph of y=-x%2B3(red) and y=%28-2%2F3%29x%2B4%2F3(green)


From the graph, we can see that the two lines intersect at the point (5,-2) (note: you might have to adjust the window to see the intersection)

d)
x%2By=-3
2x-3y=-4
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=-3

2x-3y=-4





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%2By=-3 Start with the given equation



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



1y=-x-3 Rearrange the equation



y=%28-x-3%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%28-3%29%2F%281%29 Break up the fraction



y=-x-3 Reduce



Now lets graph y=-x-3 (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+-x-3%29+ Graph of y=-x-3




So let's solve for y on the second equation


2x-3y=-4 Start with the given equation



-3y=-4-2x Subtract 2+x from both sides



-3y=-2x-4 Rearrange the equation



y=%28-2x-4%29%2F%28-3%29 Divide both sides by -3



y=%28-2%2F-3%29x%2B%28-4%29%2F%28-3%29 Break up the fraction



y=%282%2F3%29x%2B4%2F3 Reduce





Now lets add the graph of y=%282%2F3%29x%2B4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x-3%2C%282%2F3%29x%2B4%2F3%29+ Graph of y=-x-3(red) and y=%282%2F3%29x%2B4%2F3(green)


From the graph, we can see that the two lines intersect at the point (-13%2F5,-2%2F5) (note: you might have to adjust the window to see the intersection)