SOLUTION: Please help me solve this 4x4 equation w+x+y+z=2 2w-x-y+2z=7 2w+3x+2y-z=-2 3w-2x-y-3z=-2

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this 4x4 equation w+x+y+z=2 2w-x-y+2z=7 2w+3x+2y-z=-2 3w-2x-y-3z=-2      Log On


   

Question 999480: Please help me solve this 4x4 equation
w+x+y+z=2
2w-x-y+2z=7
2w+3x+2y-z=-2
3w-2x-y-3z=-2
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
w+x+y+z=2
2w-x-y+2z=7
2w+3x+2y-z=-2
3w-2x-y-3z=-2
-----
Use any method to get:
w = 1
x = 0
y = -1
z = 2
------
Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

w%2Bx%2By%2Bz=2..................eq.1
2w-x-y%2B2z=7..................eq.2
2w%2B3x%2B2y-z=-2..................eq.3
3w-2x-y-3z=-2+..................eq.4
-----------------------
w%2Bx%2By%2Bz=2..................eq.1
2w-x-y%2B2z=7..................eq.2
------------------add
w%2Bx%2By%2Bz%2B2w-x-y%2B2z=2%2B7
3w%2B3z=9
3%28w%2Bz%29=9
w%2Bz=3
w=3-z...............1a
2w%2B3x%2B2y-z=+-2.....................eq.3..multiply by 2
3w-2x-y-3z=+-2 ......................eq.4.multiply by 3
-------------------------------------------
4w%2B6x%2B4y-2z=+-4
9w-6x-3y-9z=-6+
--------------------------------add
4w%2B6x%2B4y-2z%2B9w-6x-3y-9z=+-4-6
13w%2By-11z=+-10
y=+11z-13w-10............substitute +w from 1a
y=+11z-13%283-z%29-10
y=+11z-39%2B13z-10
y=+24z-49.............1b
go to
w%2Bx%2By%2Bz=2..................eq.1, subst. w from 1a and y from 1b
%283-z%29%2Bx%2B%2824z-49%29%2Bz=2
3-z%2Bx%2B24z-49%2Bz=2
x%2B24z-46=2
x=46%2B2-24z
x=48-24z...............1c
go to
2w%2B3x%2B2y-z=+-2.........eq.3, substitute w from 1a , y from 1b, and x from 1c
2%283-z%29%2B3%2848-24z%29%2B2%2824z-49%29-z=+-2............solve for z
6-2z%2B144-72z%2B48z-98-z=+-2
-75z%2B48z%2B150-98=+-2
-27z%2B52=+-2
2%2B52=+27z
54=+27z
z=54%2F27
highlight%28z=2%29
go to 1a substitute z
w=3-z
w=3-2
highlight%28w=1%29
go to 1b substitute z
y=+24z-49.............1b
y=+24%2A2-49
y=+48-49
highlight%28y=+-1%29
go to 1c substitute z
x=48-24z...............1c
x=48-24%2A2
x=48-48
highlight%28x=0%29
so, your solutions are:
highlight%28x=0%29
highlight%28y=+-1%29
highlight%28w=1%29
highlight%28z=2%29