SOLUTION: solve by using elimination a.) 1/4x -6y=-70 5x+3/4y=49 b.) 1/4x+33/2=y y-12=-2x

Algebra ->  Equations -> SOLUTION: solve by using elimination a.) 1/4x -6y=-70 5x+3/4y=49 b.) 1/4x+33/2=y y-12=-2x      Log On


   



Question 965300: solve by using elimination
a.) 1/4x -6y=-70
5x+3/4y=49
b.) 1/4x+33/2=y
y-12=-2x

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
system%28expr%281%2F4%29x-6y=-70%2C%0D%0A++++++5x%2Bexpr%283%2F4%29y=49%29

Before using elimination, get rid of the fractions by 
multiplying them through by the least common denominator of 4:

%22%3C---%3E%22



We notice that the y terms will cancel if we multiply the second 
equation through by 8 to make the +3y become +24y. then it will
cancel with the -24y term in the first equation:


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

      x%22%22=%22%221288%2F161
      x%22%22=%22%228 

Finish by subtituting 8 for x in any of the above equations
which contain both letters.  I'll pick this one

matrix%281%2C5%2C20x%2C%22%22%2B%22%22%2C3y%2C%22%22=%22%22%2C196%29%29
matrix%281%2C5%2C20%288%29%2C%22%22%2B%22%22%2C3y%2C%22%22=%22%22%2C196%29%29
matrix%281%2C5%2C160%2C%22%22%2B%22%22%2C3y%2C%22%22=%22%22%2C196%29%29
matrix%281%2C5%2C%22%22%2C%22%22%2C3y%2C%22%22=%22%22%2C36%29%29
matrix%281%2C5%2C%22%22%2C%22%22%2Cy%2C%22%22=%22%22%2C12%29%29

The solution is (x,y) = (8,12)

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

b.) system%28expr%281%2F4%29x%2Bexpr%2833%2F2%29=y%2C%0D%0A++++++y-12=-2x%29

Multiply the first one through by 4



system%28x%2B66=4y%2Cy-12=-2x%29

Now we need to line the terms up su that the x terms come first,
the y-terms come second, the equal signs come third and the constant
terms come fourth.  We do that by adding and subtracting terms from
both sides until they get like this:



We notice that the x terms will cancel if we multiply the first 
equation through by -2 to make the x become -2x. Then it will
cancel with the 2x term in the second equation:


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

      y%22%22=%22%22144%2F9
      y%22%22=%22%2216 

Finish by subtituting 16 for y in any of the above equations
which contain both letters.  I'll pick this one

matrix%281%2C5%2C2x%2C%22%22%2B%22%22%2Cy%2C%22%22=%22%22%2C12%29%29
matrix%281%2C5%2C2x%2C%22%22%2B%22%22%2C16%2C%22%22=%22%22%2C12%29%29
matrix%281%2C5%2C%22%22%2C%22%22%2C2x%2C%22%22=%22%22%2C-4%29%29
matrix%281%2C5%2C%22%22%2C%22%22%2Cx%2C%22%22=%22%22%2C%28-4%29%2F2%29%29
matrix%281%2C5%2C%22%22%2C%22%22%2Cx%2C%22%22=%22%22%2C-2%29%29

The solution is (x,y) = (-2,16)

Edwin