USE LINEAR COMBINATIONS TO SOLVE THE LINEAR EQUATIONS 

1.

   x + 2y = 5
  3x - 2y = 7 

Since the coefficients of y are already equal in
absolute value but opposite in sign, we can add
1 times the first to 1 times the second and the
y terms will cancel

 1(  x + 2y = 5)
 1( 3x - 2y = 7)
————————————————
    4x      = 12
          x = 3

Then substitute to find y:

     x + 2y = 5
   (3) + 2y = 5
         2y = 5 - 3
         2y = 2
          y = 1



2.    x +  y =  1
     2x - 3y = 12 

Multiply the 1st equation by 3
Multiply the second by 1

  3[  x +  y =  1]
  1[ 2x - 3y = 12]

     3x + 3y =  3
     2x - 3y = 12
    —————————————
     5x      = 15
           x = 3

Then substitute to find y

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


3. x -  y = -4
   x + 2y = 5

Multiply the first equation by 2 and the second
by 1 to make the y's cancel out:

2[x -  y = -4]
1[x + 2y =  5]

  2x - 2y = -8
   x + 2y =  5
 —————————————
  3x      = -3
        x = -1 

Substitute to find y

  x + 2y = 5
 -1 + 2y = 5
      2y = 6
       y = 3

Edwin
AnlytcPhil@aol.com