Solve systems of equations using elimination method

Question

 

1.    3x+4y=8

       x+2y=10

 

2.     4x-3y=3

        3x-2y=4

 

 

Answer 1

1.    3x+4y=8
       x+2y=10
 
First, find a common coefficient of either x or y.  Let's multiply the second equation by 2 to eliminate y.
      3x + 4y = 8
      2x + 4y = 20
    --------------------  (elimination: subtract equations)
       x          = -12
       x  + 2y =  10        (second equation)
    ------------------    (eliminate x by subtracting equations)
           -2y  = -22
              y = 11      (divide both sides by -2)
 
Checking (very important):
  Is  3(-12) + 4(11) = 8    ?
        -36   + 44  = 8    ?
             8 = 8   ? yes
  Is (-12) + 2(11) = 10    ?
       -12   + 22    = 10    ?
             10 = 10    ? yes.
 
 
2.     4x-3y=3
        3x-2y=4
 
This is a little tougher, since you must multiply both equations in order to get a common coefficient of either x or y:
        12x - 9y = 9        (first equation times 3)
        12x - 8y = 16      (second equation times 4)
    ---------------------   (elimination: subtract equations)
               -y  = -7
                y = 7
               2y = 14      (multiply by 2)
          3x -2y = 4       (second equation)
       -----------------    (elimination:  add equations)
          3x      = 18
             x = 6             (divide both sides by 3)
 
Checking (very important):
  Is 4(6) -3(7) = 3    ?
       24 -21   =  3    ?
          3  =  3    ? yes
  Is 3(6) -2(7) = 4    ?
       18 - 14 = 4    ?
            4  =  4    ? yes

Answer 2

1.  Multiply the second equation by -3 and add it to the first equation

 

 3x + 4y = 9

-3x - 6y = -30

 

-2y=-21  or y=21/2 (10.5)  substitute this value for y in the second equation:

 

x + 2(21/2) = 10

 

x=-11

 

2.  Follow the same procedure for the second pair of equations, except multiply the first equation by 3 and the second by -4.