SOLUTION: 3x+6y-z=6 3x-3y+5z=-6 9x+9y-2z=11

Algebra.Com
Question 1203438: 3x+6y-z=6
3x-3y+5z=-6
9x+9y-2z=11

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
-----------------
9x+18y-3z=18
9x-9y+15z=-18
9x+9y-2z=11
----------------

Peform E1-E3 and E2-E3.

--------------
9y-z=7
-18y+17z=-29
---------------

Make 2*E1.
-------------
18y-2z=14
-18y+17z=-29
-------------

Perform E1+E2.

15z=-15


With this, you can go back and find values for y and x.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


There are an endless number of different ways to solve this system of equations; the other tutor has shown one.

Like the other tutor, I changed the three equations into equivalent forms to get "9x" as a term in all three equations. Then from there I went a different direction the they did.

[1]
[2]
[3]

Do [1]-[2] to eliminate x to get one equation in y and z; do [1]-[3] to get another.

--> [4]
[5]

Do [4]-[5] to eliminate y and solve for z




Substitute z=-1 in [5] and solve for y





Substitute z=-1 and y=2/3 in [1] to solve for x






ANSWER: (x,y,z) = (1/3,2/3,-1)


RELATED QUESTIONS

Solve the system of equations 3x+6y-z=7 3x-3y+5z=-12 9x+9y-2z=12 (answered by Fombitz)
3x+6y-z=7 2x-3y+5z=-12... (answered by josgarithmetic,math_tutor2020,greenestamps)
how do i solve; 3x-6y+5z=2 3x+3y-z=5... (answered by Alan3354)
What is the solution set: 2x+6y-z=6 4x-3y+5z=-5 6x+9y-2z=11 Thank you and Merry... (answered by jim_thompson5910)
what are the x,y,z coordinates of -7x-8y+2z=-6... (answered by Edwin McCravy)
(3x-3y)(9x-6y)= (answered by fractalier)
How do I solve the system of equations? x+2y-6=z 3y-2z=7... (answered by gonzo)
2w-3x+4y+z=7 w-x+3y-5z=10 3w+x-2y-2z=6... (answered by Alan3354)
Use Gaussian elimination. 2w-3x+4y+z=7 w-x+3y-5z=10... (answered by AnlytcPhil)