SOLUTION: solve the system of equations by graphing, then classify as consistent, or inconsistent and as dependent or independent. 5x-6y=-24 6y-5x=24 What is the solution of the sys

Algebra ->  Equations -> SOLUTION: solve the system of equations by graphing, then classify as consistent, or inconsistent and as dependent or independent. 5x-6y=-24 6y-5x=24 What is the solution of the sys      Log On


   

Question 420707: solve the system of equations by graphing, then classify as consistent, or inconsistent and as dependent or independent.
5x-6y=-24
6y-5x=24
What is the solution of the system of equations.
a. infinitely many solutions
b. no solution
c. a point
Is it consistent or inconsistent?
are the equations dependent or independent?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

5x-6y=-24
6y-5x=24
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


5x-6y=-24

6x-5y=24





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


5x-6y=-24 Start with the given equation



-6y=-24-5x Subtract 5+x from both sides



-6y=-5x-24 Rearrange the equation



y=%28-5x-24%29%2F%28-6%29 Divide both sides by -6



y=%28-5%2F-6%29x%2B%28-24%29%2F%28-6%29 Break up the fraction



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



Now lets graph y=%285%2F6%29x%2B4 (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+%285%2F6%29x%2B4%29+ Graph of y=%285%2F6%29x%2B4




So let's solve for y on the second equation


6x-5y=24 Start with the given equation



-5y=24-6x Subtract 6+x from both sides



-5y=-6x%2B24 Rearrange the equation



y=%28-6x%2B24%29%2F%28-5%29 Divide both sides by -5



y=%28-6%2F-5%29x%2B%2824%29%2F%28-5%29 Break up the fraction



y=%286%2F5%29x-24%2F5 Reduce





Now lets add the graph of y=%286%2F5%29x-24%2F5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%285%2F6%29x%2B4%2C%286%2F5%29x-24%2F5%29+ Graph of y=%285%2F6%29x%2B4(red) and y=%286%2F5%29x-24%2F5(green)


From the graph, we can see that the two lines intersect at the point (24,24) (note: you might have to adjust the window to see the intersection)



What is the solution of the system of equations.
answer: c. a point.........a point is a "solution" to the system when it
makes BOTH equations true
Is it consistent or inconsistent?
a consistent system has at least one solution; it is consistent
are the equations dependent or independent?
if dependent, graphically, this means that
one line is lying entirely on top of the other one; so they are not dependent

a system is "independent," it means that lines are not lying on
top of each other, there is EXACTLY ONE solution, and it is the point
of intersection of the two lines; so, your system is independent