SOLUTION: Graph the following system: 3x-5y=-9 5x-6y=-8 and 4x+5y=-2 4y-x+11

Algebra ->  Graphs -> SOLUTION: Graph the following system: 3x-5y=-9 5x-6y=-8 and 4x+5y=-2 4y-x+11       Log On


   

Question 120351: Graph the following system:
3x-5y=-9
5x-6y=-8
and
4x+5y=-2
4y-x+11
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:


3x-5y=-9

5x-6y=-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


3x-5y=-9 Start with the given equation



-5y=-9-3x Subtract 3+x from both sides



-5y=-3x-9 Rearrange the equation



y=%28-3x-9%29%2F%28-5%29 Divide both sides by -5



y=%28-3%2F-5%29x%2B%28-9%29%2F%28-5%29 Break up the fraction



y=%283%2F5%29x%2B9%2F5 Reduce



Now lets graph y=%283%2F5%29x%2B9%2F5 (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+%283%2F5%29x%2B9%2F5%29+ Graph of y=%283%2F5%29x%2B9%2F5




So let's solve for y on the second equation


5x-6y=-8 Start with the given equation



-6y=-8-5x Subtract 5+x from both sides



-6y=-5x-8 Rearrange the equation



y=%28-5x-8%29%2F%28-6%29 Divide both sides by -6



y=%28-5%2F-6%29x%2B%28-8%29%2F%28-6%29 Break up the fraction



y=%285%2F6%29x%2B4%2F3 Reduce





Now lets add the graph of y=%285%2F6%29x%2B4%2F3 to our first plot to get:


Graph of y=%283%2F5%29x%2B9%2F5(red) and y=%285%2F6%29x%2B4%2F3(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)




#2



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



Start with the given system of equations:


4x%2B5y=-2

4x-y=11





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


4x%2B5y=-2 Start with the given equation



5y=-2-4x Subtract 4+x from both sides



5y=-4x-2 Rearrange the equation



y=%28-4x-2%29%2F%285%29 Divide both sides by 5



y=%28-4%2F5%29x%2B%28-2%29%2F%285%29 Break up the fraction



y=%28-4%2F5%29x-2%2F5 Reduce



Now lets graph y=%28-4%2F5%29x-2%2F5 (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+%28-4%2F5%29x-2%2F5%29+ Graph of y=%28-4%2F5%29x-2%2F5




So let's solve for y on the second equation


4x-y=11 Start with the given equation



-y=11-4x Subtract 4+x from both sides



-y=-4x%2B11 Rearrange the equation



y=%28-4x%2B11%29%2F%28-1%29 Divide both sides by -1



y=%28-4%2F-1%29x%2B%2811%29%2F%28-1%29 Break up the fraction



y=4x-11 Reduce





Now lets add the graph of y=4x-11 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-4%2F5%29x-2%2F5%2C4x-11%29+ Graph of y=%28-4%2F5%29x-2%2F5(red) and y=4x-11(green)


From the graph, we can see that the two lines intersect at the point (53%2F24,-13%2F6) (note: you might have to adjust the window to see the intersection)