SOLUTION: the problem that I am solving through substitution is 9x + 2y = -51(equation 1) and -9x + y =69(equation 2), I substituted with a fraction in place of x and also got a fraction for

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: the problem that I am solving through substitution is 9x + 2y = -51(equation 1) and -9x + y =69(equation 2), I substituted with a fraction in place of x and also got a fraction for      Log On


   

Question 376347: the problem that I am solving through substitution is 9x + 2y = -51(equation 1) and -9x + y =69(equation 2), I substituted with a fraction in place of x and also got a fraction for y and it was wrong, how do I properly calculate fraction answers at this point?
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%289x%2B2y=-51%2C-9x%2By=69%29


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


%289x%2B2y%29%2B%28-9x%2By%29=%28-51%29%2B%2869%29


%289x%2B-9x%29%2B%282y%2B1y%29=-51%2B69 Group like terms.


0x%2B3y=18 Combine like terms.


3y=18 Simplify.


y=%2818%29%2F%283%29 Divide both sides by 3 to isolate y.


y=6 Reduce.


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9x%2B2y=-51 Now go back to the first equation.


9x%2B2%286%29=-51 Plug in y=6.


9x%2B12=-51 Multiply.


9x=-51-12 Subtract 12 from both sides.


9x=-63 Combine like terms on the right side.


x=%28-63%29%2F%289%29 Divide both sides by 9 to isolate x.


x=-7 Reduce.


So the solutions are x=-7 and y=6.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 9x%2B2y=-51 (red) and -9x%2By=69 (green)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim