SOLUTION: Solve by substitution or elimination: 5x+2y+10z=5 3x-y+5z=-6 2x-3y-7z=5

Solve by substitution or elimination:

5x + 2y + 10z =  5
3x -  y +  5z = -6
2x - 3y -  7z =  5

1. Pick a pair of equations and a letter to eliminate:

I'll pick the first two equations and I'll pick y
to eliminate from them:

5x + 2y + 10z =  5
3x -  y +  5z = -6

I can eliminate y by multiplying the second equation
through by 2 and adding vertically term by term:

 5x + 2y + 10z =   5
 6x - 2y + 10z = -12
--------------------
11x      + 20z =  -7

2. Pick a DIFFERENT pair of equations but the SAME 
letter to eliminate:  

I'll pick the last two equations and I must eliminate
y from them:

3x -  y +  5z = -6
2x - 3y -  7z =  5


I can eliminate y by multiplying the upper equation  
through by -3 and adding vertically term by term:

-9x + 3y - 15z = 18
 2x - 3y -  7z =  5
-------------------
-7x      - 22z = 23

Next we put those two equations in which we have
eliminated y together:

-7x - 22z = 23
11x + 20z = -7

We can eliminate x by multiplying the upper
equation by 11 and the bottom one by 7

-77x - 242z = 253
 77x + 140z = -49
-----------------
      -102z = 204
          z = -2

Substitute z = -2 into 

   -7x - 22z =  23
-7x - 22(-2) =  23
    -7x + 44 =  23
         -7x = -21
           x = 3

Substitute z = -2 and x = 3 into one
of the original three equations:

   3x -  y +  5z = -6
3(3) - y + 5(-2) = -6 
      9 - y - 10 = -6
          -y - 1 = -6
              -y = -5
               y = 5 

(x, y, z) = (3, 5, -2) 

Edwin