SOLUTION: If possible, solve the system of equations. Use any method. If there is not unique solution to the system, state the reason 2x-9y=9 (1) -18x+81y= -81 (2) What is the

Algebra ->  Linear-equations -> SOLUTION: If possible, solve the system of equations. Use any method. If there is not unique solution to the system, state the reason 2x-9y=9 (1) -18x+81y= -81 (2) What is the       Log On


   

Question 172174: If possible, solve the system of equations. Use any method. If there is not unique solution to the system, state the reason
2x-9y=9 (1)
-18x+81y= -81 (2)
What is the solution to this system?
Type an ordered pair. Type N if there is no solution. Type I if there is infinitely many solutions.
Which of the statements below is a good explanation for the solution?
The graphs intersect at one point, so the solution is unique.
The graphs of two equations represent the same line.
The graphs of the two equations never intersect.
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%282x-9y=9%2C-18x%2B81y=-81%29


9%282x-9y%29=9%289%29 Multiply the both sides of the first equation by 9.


18x-81y=81 Distribute and multiply.


So we have the new system of equations:
system%2818x-81y=81%2C-18x%2B81y=-81%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2818x-81y%29%2B%28-18x%2B81y%29=%2881%29%2B%28-81%29


%2818x%2B-18x%29%2B%28-81y%2B81y%29=81%2B-81 Group like terms.


0x%2B0y=0 Combine like terms. Notice how the x terms cancel out.


0=0Simplify.


Since 0=0 is ALWAYS true, this means that there are an infinite number of solutions. So the system is consistent and dependent.


Graphically, these two equations are really the SAME equation. So this means that there are an infinite number of intersections.