SOLUTION: Solve the system if possible. 2x-4y+2z=11 x+3y-2z=-9 4x-2y+z=7

Question 64107This question is from textbook College Algebra with Modeling and Visualization
: Solve the system if possible.
2x-4y+2z=11
x+3y-2z=-9
4x-2y+z=7 This question is from textbook College Algebra with Modeling and Visualization

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
This one can be solved without using the matrice
:
eq 1: 2x - 4y + 2z = 11
eq 2: x + 3y - 2z = -9
eq 3: 4x - 2y + z = 7
:
Adding equations 1 & 2 eliminates z
2x - 4y + 2z = 11
x + 3y - 2z = -9
------------------ add
3x - x + 0 = 2
3x - y = 2
:
Mult eq 3 by 2 and add it to eq 2, eliminating z again
8x - 4y + 2z = 14
x + 3y - 2z = -9
------------------ add
9x - y + 0 = 5
9x - y = 5
:
Subtract (3x - y = 2) from the above equation:
9x - y = 5
3x - y = 2
-------------subtract
6x + 0 = 3
x = 3/6
x = .5
:
Use 9x - y = 5 to find y, substitute .5 for x
9(.5) - y = 5
4.5 - y = 5
-y = 5 - 4.5
-y = .5
y = - .5
:
Find z using eq 2:
x + 3y - 2z = -9
.5 + 3(-.5) - 2z = -9
.5 - 1.5 - 2z = -9
-1 - 2z = -9
Get rid all those negative, mult eq by -1
1 + 2z = 9
2z = 9 -1
z = 8/2
z = +4
:
Our solution: x = +.5; y = -.5; z = +4
You can check it in equations 1 or 3:

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