SOLUTION: -11x - 3y - 10z = 17 -12x - 5y + 2z = 84 3x - 6y + 3z = 51 I need to solve this system of linear equations using any method. I'd like to see the steps and the correct answer.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: -11x - 3y - 10z = 17 -12x - 5y + 2z = 84 3x - 6y + 3z = 51 I need to solve this system of linear equations using any method. I'd like to see the steps and the correct answer.      Log On


   

Question 160344: -11x - 3y - 10z = 17
-12x - 5y + 2z = 84
3x - 6y + 3z = 51
I need to solve this system of linear equations using any method. I'd like to see the steps and the correct answer. I'm not sure which method would be the easiest and I'm just stuck. Thank you for all your help.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
reduce (simplify) where you can __ dividing 3rd eqn by 3 gives a NEW 3rd eqn __ x-2y+z=17

new 3rd eqn times 10, added to 1st eqn __ -x-23y=187 __ -23y-187=x

new 3rd eqn times -2, added to 2nd eqn __ -14x-y=50

substituting __ -14(-23y-187)-y=50 __ 321y=-2568 __ y=-8

substituting __ -23(-8)-187=x __ -3=x

substituting __ (-3)-2(-8)+z=17 __ z=4