SOLUTION: 1) Solve the system of equations by graphing. Then classify the system as consistent or inconsistent as dependent or independent. 7x-9y=-18 9y-7x=18 What is the solution

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 1) Solve the system of equations by graphing. Then classify the system as consistent or inconsistent as dependent or independent. 7x-9y=-18 9y-7x=18 What is the solution      Log On


   

Question 146896: 1) Solve the system of equations by graphing. Then classify the system as consistent or inconsistent as dependent or independent.
7x-9y=-18
9y-7x=18

What is the solution of the system of equations?
a) Infinitely many solutions
b) No solution
c) A point

Is the system consistent or inconsistent?

Are the equations dependent or independent?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%287x-9y=-18%2C9y-7x=18%29


In order to graph these equations, we must solve for y first.


Let's graph the first equation:


7x-9y=-18 Start with the first equation.


-9y=-18-7x Subtract 7x from both sides.


y=%28-18-7x%29%2F%28-9%29 Divide both sides by -9 to isolate y.


y=%287%2F9%29x%2B2 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%287%2F9%29x%2B2.


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


Now let's graph the second equation:


9y-7x=18 Start with the second equation.


9y=18%2B7x Add 7x to both sides.


y=%2818%2B7x%29%2F%289%29 Divide both sides by 9 to isolate y.


y=%287%2F9%29x%2B2 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%287%2F9%29x%2B2.


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


Now let's graph the two equations together:


Graph of y=%287%2F9%29x%2B2 (red). Graph of y=%287%2F9%29x%2B2 (green)


From the graph, we can see that one line is right on top of the other one, which means that they intersect an infinite number of times. So there are an infinite number of solutions. This means that the system of equations is consistent and dependent.