SOLUTION: solve the following system of linear equations for x,y and z. x-2y+3z=-11 2x-z=8 3y+z=10

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: solve the following system of linear equations for x,y and z. x-2y+3z=-11 2x-z=8 3y+z=10       Log On


   

Question 1121369: solve the following system of linear equations for x,y and z.
x-2y+3z=-11
2x-z=8
3y+z=10
Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x-2y%2B3z=-11.....(1)
2x-z=8.....(2)
3y%2Bz=10.....(3)
start with (2) and (3)
2x-z=8.....(2)
3y%2Bz=10.....(3)............. add them
-------------------------------------------
2x-z%2B3y%2Bz=8%2B10
2x%2B3y=18.........(a)
go with (1) and (3)
x-2y%2B3z=-11.....(1)
3y%2Bz=10.....(3)............both sides multiply by 3
--------------------------------------
x-2y%2B3z=-11.....(1)
9y%2B3z=30.....(3)
-------------------------------------------------.................subtract (3) from (1)
x-2y%2B3z-%289y%2B3z%29=-11-30
x-2y%2B3z-9y-3z=-41
x-11y=-41...........(b)
go with (a) and (b)
2x%2B3y=18.........(a)
x-11y=-41...........(b).......both sides multiply by 2
--------------------------------
2x%2B3y=18.........(a)
2x-22y=-82...........(b)
--------------------------------------------------subtract (b) from (a)
2x%2B3y+-%282x-22y%29=18-%28-82%29
2x%2B3y+-2x%2B22y=18%2B82
3y+%2B22y=100
25y=100
y=100%2F25
highlight%28y=4%29
go back to x-11y=-41...........(b), substitute 4 for y
x-11%2A4=-41
x-44=-41
x=44-41
highlight%28x=3%29
finally, go to 2x-z=8.....(2), substitute 3 for x
2%2A3-z=8
6-8=z
highlight%28z=-2%29

solutions:
highlight%28x=3%29
highlight%28y=4%29
highlight%28z=-2%29


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


How do you want it done? Substitution? Cramer's Rule? Gauss-Jordan?

I'm not going to do it all three ways, and besides, you need to learn to follow instructions. For example, the instructions on the page where you submitted your problem that say to ask a complete question, to explain what it is about the problem that is giving you difficulty, and to show the work you have done so far.


John

My calculator said it, I believe it, that settles it