Systems Question- Elimination

Question

Here are the equations:

1/2x+1/3y=-4

1/5x+1/5y=-2

 

Can someone solve this using the elimination method?

 

Ty!!

Answer 1

(1) To Eliminate a variable, we set its coefficient either the same (then subtract equations) or opposite (then add equations).

 

(2) When the coefficients are fractions, we may multiply the entire equation by the LCD of the fractions in order to make integer coefficients.

 

 

O.K. given:

    (1/2)x  +  (1/3)y  =  -4

    (1/5)x  +  (1/5)y  =  -2

 

 we can change to:

      3x      +     2y     =  -24             [eq 1]

       x       +      y     =   -10             [eq 2]

 

  then to:

       3x     +     2y    =   -24

       2x     +     2y    =   -20

 ----------------------------------    [elimination; subtract equations]

        x                     =    -4

 

       x       +     y     =   -10                    [eq2 again]

  --------------------------------     [elimination method; subtract equations]

                    - y     =      6

                      y     =     -6

 

Check:

    Does    (1/2)(-4)  +  (1/3)(-6)  =   -4    ?

                    -2           -2                   =  -4   ?

                           -4                          =  -4    ?yes

    Does    (1/5)(-4)   +  (1/5)(-6)  =   -2    ?

                 (1/5)(-10)  =  -2   ?                 [use distributive property]

                      -2         =    -2    ?yes