SOLUTION: Please help me solve the following for x, y, and z. and please show the work. 3x+2y+z=8 2x-3y+2z=-16 x+4y-z=20

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Question 1027945: Please help me solve the following for x, y, and z. and please show the work.
3x+2y+z=8
2x-3y+2z=-16
x+4y-z=20
Found 3 solutions by josgarithmetic, mananth, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Try either Elimination Method, or row reduction operations (matrices), since so many variables.




Exchange R1 and R3.


R2=R2-2*R1;
R3=R3-3*R1.
----



R2=-1*R2, R3=-1*R3.
---


(1/2)*R3




R3=R3-R2
---


R2 *(1/5) and R3* (-1/2)
-


This is still not finished, but at this point shows .
Continue with row operations, now moving upward; Let R2=R2+4*R3; and let R1=R1+R3; and you will see the partial result indicating . Solve for x from that any way you like.
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
By elimination method
3 x + 2 y + 1 z = 8 -------------- 1
2 x + -3 y 2 z = -16 -------------- 2
1 x + 4 y + -1 z 20 -------------- 3

consider equation 1 &2 Eliminate y
Multiply 1 by 3 -5
Multiply 2 by 2 4
we get
9 x + 6 y + 3 z = 24
4 x + -6 y + 4 z = -32
Add the two
13 x + 0 y + 7 z = -8 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 4
Multiply 3 by 3
we get
8 x + -12 y + 8 z = -64
3 x + 12 y + -3 z = 60
Add the two
11 x + 0 y + 5 z = -4 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by -11
Multiply (5) by 13
we get
-143 x + -77 z = 88
143 x + 65 z = -52
Add the two
0 x + -12 z = 36
/ -12
z = -3





Plug the value of z in (5)
11 x + 5 z = -4
11 x = 11
x = 1
x=1, z=-3
Plug the values to get y
y=4
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Please help me solve the following for x, y, and z. and please show the work.
3x+2y+z=8
2x-3y+2z=-16
x+4y-z=20
3x + 2y +  z =    8 ------ eq (i)

2x – 3y + 2z = - 16 ------ eq (ii)

 x + 4y –  z =   20 ------ eq (iii)

4x + 6y = 28 ---------- Adding eqs (i) & (iii) ------- eq (iv)

2x + 8y – 2z = 40 ----- Multiplying eq (iii) by 2 ---- eq (v)

4x + 5y = 24 ---------- Adding eqs (v) & (ii) -------- eq (vi)

 -------- Subtracting eq (vi) from eq (iv)



4x + 6(4) = 28 -------- Substituting 4 for y in eq (iv)

4x + 24 = 28

4x = 4

x = , or 



1 + 4(4) – z = 20 --------- Substituting 1 for x and 4 for y in eq (iii)

1 + 16 – z = 20

17 – z = 20

- z = 20 – 17

z = , or  

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