SOLUTION: Solve each system algebraically. Explain why you chose the method you used. x^2-48/9x+1/3y+1/3=0 -5/4x^2-3/2x+1/4y-1/2=0 Thankkk youuu :DDDD

Algebra ->  Systems-of-equations -> SOLUTION: Solve each system algebraically. Explain why you chose the method you used. x^2-48/9x+1/3y+1/3=0 -5/4x^2-3/2x+1/4y-1/2=0 Thankkk youuu :DDDD      Log On


   



Question 878182: Solve each system algebraically. Explain why you chose the method you used.
x^2-48/9x+1/3y+1/3=0
-5/4x^2-3/2x+1/4y-1/2=0
Thankkk youuu :DDDD

Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry, there is no equal sign in the second one, so it
isn't an equation.  Also there is no x term either but two number
terms, -3/2 and -1/2.  I think you meant one of those to
have an x by it right?  Type it carefully and correctly in the 
thank-you note and I'll get back to you.

Edwin

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
I just guessed and put in an x and an equal sign in the second one.



Reduce the fraction 48%2F9 to 16%2F3



Multiply the first one through by 3 and the
second one through by 4

system%283x%5E2-16x%2By%2B1=0%2C%0D%0A-5x%5E2-6x%2By-2=0%29

Solve each for y:

system%28y+=+-3x%5E2%2B16x-1%2C%0D%0Ay+=+5x%5E2%2B6x%2B2%29

St the right sides equal

-3x%5E2%2B16x-1%22%22=%22%225x%5E2%2B6x%2B2%29 

Get 0 on the left side:

0%22%22=%22%228x%5E2-10x%2B3%29

Factor the right side:

0%22%22=%22%22%282x-1%29%284x-3%29%29

2x-1 = 0;    4x-3 = 0
  2x = 1       4x = 3
   x = 1%2F2;       x = 3%2F4
 
Substituting     x = 1%2F2 in

y%22%22=%22%22-3x%5E2%2B16x-1

y%22%22=%22%22-3%281%2F2%29%5E2%2B16%281%2F2%29-1

y%22%22=%22%22-3%281%2F4%29%2B8-1

y%22%22=%22%22-3%2F4%2B7

y%22%22=%22%22-3%2F4%2B28%2F4

y%22%22=%22%2225%2F4

So one solution is (x,y) = %28matrix%281%2C3%2C1%2F2%2C+%22%2C%22%2C+25%2F4%29%29      
  
-----

Substituting     x = 3%2F4 in

y%22%22=%22%22-3x%5E2%2B16x-1

y%22%22=%22%22-3%283%2F4%29%5E2%2B16%283%2F4%29-1

y%22%22=%22%22-3%289%2F16%29%2B12-1

y%22%22=%22%22-27%2F16%2B11

y%22%22=%22%22-27%2F16%2B176%2F16

y%22%22=%22%22149%2F16

So the other solution is (x,y) = %28matrix%281%2C3%2C3%2F4%2C+%22%2C%22%2C+149%2F16%29%29     

Edwin