SOLUTION: How do I solve this? I've tried by susbtitution and elimination without success. (1/3)x - (3/2)y = -5 (3/4)x + (1/3)y = 11 Thank you!

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: How do I solve this? I've tried by susbtitution and elimination without success. (1/3)x - (3/2)y = -5 (3/4)x + (1/3)y = 11 Thank you!      Log On


   

Question 79185This question is from textbook College Algebra
: How do I solve this? I've tried by susbtitution and elimination without success.
(1/3)x - (3/2)y = -5
(3/4)x + (1/3)y = 11
Thank you! This question is from textbook College Algebra

Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
sometimes, eliminating the fractions will make things easier ... multiplying the first equation by 6 gives 2x-9y=-30

multiplying the second equation by 12 gives 9x+4y=132 ... multiplying again by 9 gives 81x+36y=1188

multiplying the first equation again by 4 gives 8x-36y=-120 ... adding equations gives 89x=1068 , so x=12 and y=6

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2F3%29x+-+%283%2F2%29y+=+-5
%283%2F4%29x+%2B+%281%2F3%29y+=+11

You should clear of fractions first.

Clear the first of fractions by multiplying 
through by 6%2F1: 

%286%2F1%29%281%2F3%29x+-+%286%2F1%29%283%2F2%29y+=+%286%2F1%29%28-5%29

   2x - 9y = -30

Clear the second of fractions by multiplying 
through by 12%2F1: 

%2812%2F1%29%283%2F4%29x+%2B+%2812%2F1%29%281%2F3%29y+=+%2812%2F1%29%2811%29

   9x + 4y = 132

So we have the system

   2x - 9y = -30
   9x + 4y = 132

The coefficients of y are -9 and 4. The LCD of
their absolute values is 36, so 

1. We need to make the -9 in the first into a -36 
by multiplyng the whole first equation through by 4.
2. We need to make the 4 in the second into a 36 
by multiplyng the whole second equation through by 9.

(4)2x - (4)9y = (4)(-30)
(9)9x + (9)4y = (9)(132)

which simplified becomes:

     8x - 36y = -120
    81x + 36y = 1188

Add term by term vertically

     8x - 36y = -120
    81x + 36y = 1188
   ------------------
    89x       = 1068

Divide through by 89

            x = 1068/89
            x = 12

Sunstitute 12 for x in

    2x - 9y = -30

 2(12) - 9y = -30
    24 - 9y = -30
        -9y = -30 - 24
        -9y = -54
          y = (-54)/(-9)
          y = 6

So the solution is (x,y) = (12,6).

Edwin