solve by elimination

Question

{5x-2y=-15
{3x+8y=37

Answer 1

The elimination method eliminates one of the variables by adding/subtracting terms with the same (or opposite) coefficient.  So, we many have to multiply one or both equations so that either the x-coefficient or the y-coefficient allows us to eliminate that term.

 

Let's eliminate the x term and solve for y first:

     15x  -   6y =  -45           [multiply first equation by 3]

     15x + 40y =  185            [multiply second equation by 5]

  ------------------------          [elimination: subtract equations]

            - 46y  = -230

               y =  5                    [divide both sides by -46]

 

At this point, you may use that answer with either equation and do the elimination of y.  It is also permissible to substitute the answer value for y into either equation and solve for x.

 

However, let's use elimination using the original equations and eliminate y.

     20x   -  8y   =  -60              [multiply first equation by 4]

       3x  +  8y  =    37              [second equation]

  -----------------------------    [elimination:  add equations]

     23x           =    -23

               x = -1                    [divide both sides by 23]

 

Checking (very important):

  Is 5(-1) - 2(5) = -15  ?

       -5  -10   = -15   ?

         -15      = -15   ?  yes

  Is 3(-1) + 8(5) = 37   ?

       -3   +  40   = 37   ?

             37  =  37   ?  yes

Answer 2

Hi Joy, set up the two equations:

 

5x  -  2y  = -15

3x  + 8y  =  37

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

 

Multiply the first equation by 4 and add:

 

20x - 8y = -60
 3x + 8y =  37
-----------------

23x        = -23

 

Divide both sides by 23:

 

x = -1

 

Substitute for x in the first equation:

 

-5 * 1 - 2y = -15

 

-5 - 2y = -15

 

Add 5 to both sides:

 

-2y = -10

 

Divide both sides by -2:

 

y = 5

 

Solution:

 

x = -1, y = 5

 

Check:

 

Substitute for x and y in the second equation:

 

3 * -1 + 8 * 5 = 37

 

-3 + 40 = 37

 

37 = 37, values check.

 

Questions?