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Well I will start off saying I know I have the wrong answer somewhere and I know that because I put my answers into the original equations and they don't work. I have trouble when you throw that third variable in so if someone can tell what is right (if anything) and where I went wrong. Thanks!! Andrea

(a)
2x – y + z = 8
x + 2y + z = -3
x - 2y – z = 7

(1 & 3)
3x – 3y = 15
x – y = 5

2x = 4
x = 2

2 – y = 5
y = -3

2 + 2(-3) + z = -3
z = 1

(b)
3x - y - 2z = 11
x – 2y + 3z = 12
x + y - 2z = 5

(1 & 3) = (4)
4x – 4z = 16

(2 & 3) = (5)
x – 2y + 3z = 12
2x + 2y – 4z = 10
3x + z = 22

(4 & 5)
4x – 4z = 16
3x + z = 22

4x – 4z = 16
-12x + 4z = -88
-8x = -72
x = 9

3(9) + z = 22
27 + z = 22
z = -5

9 – y – 2(-5) = 5
9 – y + 10 = 5
19 – y = 5
-y = -14
y = 14
 
I looked at the first.

I find your methodology a bit difficult to follow, but your answers are correct. There must be some difficulty with your arithmetic while checking.

Document more and be more careful and deliberate.
 
a) I'm sorry, but I can't follow your steps. The "1&3" notation means, I think, that you added the first and third lines, and then simplified. But I can't see where the "2x = 4" is coming from...?

b) I think the "(1&3)=(4)" notation means "adding the first and third lines gives me this fourth, new, equation". I think the "(2&3)=(5)" notation means "multiplying the third line by 2 and adding this to the second line gives me this fifth, new, equation". But 3z - 4z = -z, not +z.

Eliz.
 
Ok, I tried to notate what I was doing better for these two problems. Thanks!!

(A)
2x – y + z = 8
x + 2y + z = -3
x - 2y – z = 7

(Add 1 & 3; 4)
3x – 3y = 15
x – y = 5

(Add 2 & 3)
2x = 4
x = 2

(Substitute into 4)
2 – y = 5
y = -3

(Substitute into 2)
2 + 2(-3) + z = -3
z = 1

(B)
3x - y - 2z = 11
x – 2y + 3z = 12
x + y - 2z = 5

(Add 1 & 3; 4)
4x – 4z = 16

(Add 2 & 3 doubled; 5)
x – 2y + 3z = 12
2x + 2y – 4z = 10
3x + z = 22

(Add 4 & 5 quadrupled)
4x – 4z = 16
3x + z = 22

4x – 4z = 16
-12x + 4z = -88
-8x = -72
x = 9

(Substitute into 5)
3(9) + z = 22
27 + z = 22
z = -5

(Substitute into 3)
9 – y – 2(-5) = 5
9 – y + 10 = 5
19 – y = 5
-y = -14
y = 14
 
a) Your solution, (x, y, z) = (2, -3, 1), is correct.

b) Check your second step: 3z - 4z is not 1z.

Eliz.
 
Eliz

I reworked the problem from the point you said because I did see where I did my math incorrectly however I ended up with the same result which does not work when I plug it back into the original. Perhaps I am just overlooking at what is wrong. Thanks. Andrea

3x - y - 2z = 11
x – 2y + 3z = 12
x + y - 2z = 5

(Add 1 & 3; 4)
4x – 4z = 16
x – z = 4

(Add 2 & 3 doubled; 5)
x – 2y + 3z = 12
2x + 2y – 4z = 10
3x – z = 22

(Add 4 & 5)
x – z = 4
3x – z = 22

x – z = 4
-(3x – z = 22)

x – z = 4
-3x + z = -22

-2x = -18
x = 9

(Substitute into 5)
3(9) + z = 22
27 + z = 22
z = -5

(Substitute into 3)
9 – y – 2(-5) = 5
9 – y + 10 = 5
19 – y = 5
-y = -14
y = 14
 
Andrea, following by you is correct:

3x - y - 2z = 11
x – 2y + 3z = 12
x + y - 2z = 5

(Add 1 & 3; 4)
4x – 4z = 16
x – z = 4

(Add 2 & 3 doubled; 5)
x – 2y + 3z = 12
2x + 2y – 4z = 10
3x – z = 22

(Add 4 & 5)
x – z = 4
3x – z = 22

x – z = 4
-(3x – z = 22)

x – z = 4
-3x + z = -22

-2x = -18
x = 9
.......................................................................................................

This is another way of doing same thing:

3x - y - 2z = 11 [1]
x – 2y + 3z = 12 [2]
x + y - 2z = 5 [3]

[1] + [3]:
4x – 4z = 16
x – z = 4 [4]

[2] + 2*[3]:
x – 2y + 3z = 12
2x + 2y – 4z = 10
3x – z = 22 [5]

[4]: z = x - 4
[5]: z = 3x – 22

3x - 22 = x - 4
2x = 18
x = 9

Actual numbering the equations makes it easier to follow (as Stapel said)

Handling [4] and [5] as I did is not a must: but saves time and is easier.
 
acjordan said:
I reworked the problem from the point you said because I did see where I did my math incorrectly however I ended up with the same result....
Click to expand...
Two errors somehow cancelled out on the x-value...? But then you used the same (incorrect) equation when finding the z-value:

. . . . .original equation 5: 3x + z = 22

. . . . .corrected equation 5: 3x - z = 22

. . . . .equation used after solving for x:
. . . . .3x + z = 22

This still needs to be corrected.

Eliz.
 
Go all the way back up to the top and review this instruction: "...be more careful and deliberate."
 
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