Algebra-System of equations

Question

3x+4y=3

3x+2y=9

 

Solve the system of equations using elimination

Answer 1

The elimination method adds or subtracts a common term from two equations.

For this problem, we already have 3x in each equation, but we could get 4y in each if we wanted to.

      3x + 4y = 3         {eq1)

      3x + 2y = 9         (eq2)

   ------------------      (subtract equations to eliminatex term)

      0   + 2y  = -6

               y = -3         (divide both sides by 2; eq3)

 

        3x + 2y = 9       (eq2 again; we could use either eq1 or eq2 again)

                2y = -6        (multiply eq3 by 2)

     ------------------      (subtract equations to eliminatey term)

         3x       = 15

             x =  5         (divide both sides by 3)

 

Checking (very important:

   Is    3x+ 4y = 3          ?

        3(5) + 4(-3) = 3      ?

             15 – 12 = 3       ?

                  12 = 12  ?    Yes.

Is   3x + 2y = 9    ?

    3(5) + 2(-3) = 9    ?

     15 – 6 = 9    ?

       9 = 9      ?     Yes.

Answer 2

Hi Mary,

 

Lets solve this by an initial subtraction operation.

when you do this, the equations will look like this:

 

 

   3x+4y=3
(-)3x+2y=9        ----------------(subtracting by initially putting a minus sign before the entire equation, because of this, 

                                                the entire equations signs will change.

=>

3x+4y=3
-3x-2y=-9

 

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

0 + 2y = -6

 

=> y = -6 = -3

            2

substituting this value of y in any of the initial 2 equations

3x + 4y = 3

3x + 4 (-3) = 3

=> 3x = 3 + 12 = 15

=> x = 15 = 5

            3

 

therefore x = 5, y =-3 is the solution

 

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

 

Another method:

 

3x+4y=3  ----------(1)
3x+2y=9  ----------(2)

 

from (1)  3x = 3-4y

from (2)  3x = 9-2y

 

equating both because both have a common value 3x

 

3-4y = 9-2y

 

pulling like terms together

 

-4y+2y = 9-3

=>-2y = 6

=> y = -6/2 = -3

 

substituting this value in any of the above initial equations: 

 

3x = 3-4y

=> 3x = 3 - 4 (-3) = 15

=> x = 15/3 = 5

 

therefore x = 5, y =-3 is the solution

 

Please let me know if you need any further clarification.