Question 102566
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Use the elimination method to find all solutions of the system;

A. 5x+2y=-19
   7x+3y=-27
   x=___  y=____

    Let us eliminate x to solve for y. the equations are:

       5x + 2y = -19    eqn 1
       7x + 3y = -27    eqn 2

    To eliminate x, multiply -7 to eqn 1 and 5 to eqn 2. 

      -7 (5x + 2y = -19)
       5 (7x + 3y = - 27)

       -35x - 14y =  133   eqn 1
        35x + 15y = -135   eqn 2
     
    Add eqn 1 and eqn 2, answer is:

       -35x - 14y =  133   eqn 1
        35x + 15y = -135   eqn 2
       __________________________
         0  -   y = -2

    Therefore y = -2. Substitute y = -2 to eqn 1 or eqn 2 to find x.

           5x + 2y = -19, y = -2
        5x + 2(-2) = -19
            5x - 4 = - 19          Add 4 both sides.
        5x - 4 + 4 = -19 + 4 
                5x = -15           Divide both sides by 5 so x will be left.
                 x = -3 

Therefore x = -3 and y = -2

 You try b - d. 
  
b. x+3y=5
   6y+z=12
   x-2x=10

   Find the simpliest eqn first. look at x - 2x = 10. with this you can 
   solve for x.

     x - 2x = 10
         -x = 10    divide -1 both sides to make x positive.
          x = -10

   Since you have the value of x, you can substitute it to the eqn x + 3y = 5
     
         x + 3y = 5, where x = -10
       -10 + 3y = 5                 Add 10 both sides
  -10 + 10 + 3y = 5 + 10
             3y = 15                Divide both sides by 3
              y = 5

   Now you can solve for z using y = 5 and the eqn 6y+z=12.
 
         6y + z = 12 , where y = 5
       6(5) + z = 12
         30 + z = 12                Subtract both sides by 30
    30 - 30 + z = 12 - 30
              z = -18

   Therefore x = -10, y = 5 and z = -18