Elimination Methods

Question

5x - 3y = 20 & 2x + 3y = 15

 

Hi,

How do I solve this equation using the elimination method? 

Thanks

:) 

Answer 1

The Elimination Method eliminates one of the variables, so you have a value for the other.  Then, you may either Eliminate that variable or use the Substitution Method to find the value of the other variable.

 

Since either Addition or Subtraction is used in the Elimination Method, you must first multiply one or both of the equations by a constant so that one of the coefficients is the same or is the negative of the other coefficient for that variable.

 

      5x    -   3y    =    20

      2x   +   3y    =    15

   -----------------------------    [Elimination Method; ADD equations]

      7x                =    35

        x                =     5           [divide both sides by 7]

 

       2x     +  3y  =    15

       2x               =    10        [Multiply the answer for x by 2]

      ------------------------      {Elimination; SUBTRACT equations]

                    3y  =     5

                     y   =  5/3

 

 

Check:

     Is   5(5) - 3(5/3) = 20   ?

            25  -  5 = 20   ?

              20  =  20   ?yes

     Is   2(5) + 3(5/3) = 15   ?

            10  +  5  = 15   ?

              15  =  15   ?yes

Answer 2

Pick one equation and solve it for y.

Substitute for y in the other equation, thus solving for x.

 

It's always like that.