SOLUTION: Solve the system of equations algebrically. Eliminate the z variable. 2x-y+4z=-2 3x-2y-z=-3 x+4y+2z=17

Question 54320This question is from textbook mathematics in action
: Solve the system of equations algebrically.
Eliminate the z variable.
2x-y+4z=-2
3x-2y-z=-3
x+4y+2z=17 This question is from textbook mathematics in action

Found 2 solutions by venugopalramana, funmath:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Solve the system of equations algebrically.
Eliminate the z variable.
2x-y+4z=-2...............................I
3x-2y-z=-3......................................II
x+4y+2z=17...............................III
EQN.III+2*EQN.II
X+4Y+2Z+6X-4Y-2Z=17-6=11
7X=11.............X=11/7
EQN.I-2*EQN.III
2X-Y+4Z-2X-8Y-4Z=-2-34=-36
-9Y=-36
Y=4
SUBSTITUTING IN EQN.I
2*11/7 -4 +4Z = -2
4Z = -8/7
Z=-2/7
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
2x-y+4z=-2 (E1)
3x-2y-z=-3 (E2)
x+4y+2z=17 (E3)
: Eliminate z in (E1) and (E2) by multiplying 4*(E2) and adding the two equations.
2x-y+4z=-2----------> 2x- y+4z=-2
4(3x-2y-z)=4(-3)---->12x-8y-4z=-12
:
2x- y+4z=-2
12x-8y-4z=-12
_____________
14x-9y+0z=-14
14x-9y=-14 (E4)
:Eliminate the z using 2*(E2) + (E3).
2(3x-2y-z)=2(-3)------->6x-4y-2z=-6
x+4y+2z=17-------------> x+4y+2z=17
:
6x-4y-2z=-6
+x+4y+2z=17
_____________
7x+0y+0z=11
7x=11
7x/7=11/7
x=11/7
:Substitute x=11/7 into (E4) and solve for y:
14(11/7)-9y=-14
Clear the fraction by multiplying everything by 7 to make it easier to solve.

154-63y=-98
-154+154-63y=-98-154
-63y=-252
-63y/-63=-252/-63
y=4
:
Substitute x=11/7 and y=4 into (E2).
3(11/4)-2(4)-z=-3
Work that out and you get z=-2/7
So your answer is (11/7,4,-2/7)
Don't forget to check your answer by sustituting these values into all three original equations.
Let me know if you need more explanation.
Happy Calculating!!!
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