SOLVING FOR TWO UNKNOWNS WITH TWO EQUATIONS.
METHOD A: THE SUBSTITUTION METHOD.
   1. solve one equation for one of the unknowns (variables).
   for example:  X+2Y = 12
   What does X equal?  X =-2Y+12  (SUBTRACT 2Y FROM BOTH SIDES OF EQUATION)
   2. Substitute the value for X in the second equation as follows:
      Second equation is  X-Y=0
                 -2Y+12-Y=0 (ADD THE Y'S AND SUBTRACT 12 FROM BOTH SIDES)
                 -3Y=-12  (DIVIDE BOTH SIDE BY 3)
                  -Y=-4  (MULTIPLY BOTH SIDES BY -1)
                   Y=4
   3. Solve for X using the first equation and Y=4
                  X+2Y=12
                  X+2*4=12
                  X=4
   4. Enter the values in the second equation to verify answer.
                  X-Y=0
                  4-4=0
METHOD B:THE LINEAR COMBINATION METHOD
 1.  To do this method you must combine the two equations to 
   eliminate the x's or y's
 2.  To do this you must make the numerical coefficients in front
   of the x's or y's the same in both equations.
 3.  Then you can add or subtract the two equations to eliminate
   one of the variables.
   For example #1: 
                x+2y=12
     subtract   x- y =0 (subtract the x's,subtract the y's,subtract 0)
                -------
                  3y =12 (divide both sides by 3)
                   y = 4
       example #2:
               3x+2y=12
               4x+ y=11
       first, multiply the first equation by the numerial coefficient
              of x of the second  equation:
              (4) 3x+2y=12  equals 12x+8y=48
       second, multiply the second equation by the numerical coefficient
               of x of the first equation:
               (3)  4x+y=11 equals 12x+3y=33
       third,  subtract the two new equations:
                  12x+8y=48           12x 8y= 48
         subtract 12x+3y=33  do this -12x-3y=-33
                  ---------           ----------
                      5y=15               5y= 15
                                           y= 3
END