please help check my work

[milanna]

determine if the given ordered triple is a solution of the system (-3, -5, 3)

x+4y+4z = -29
3y+3z = -24
z = -3



3y + 3z = -24
3y + 3(-3) = -24
3y -9 = -24
3y = -15
y=-5


x + 4y + 4z = -29
x + 4(-5) + 4(-3) = -29
x - 20 - 12 = -29
x - 32 = -29
x = 3


so I get x=3 y=-5 z=-3

Then the given ordered triple (-3, -5, 3) IS a solution of the system?
Thanks

 

[Gene]

I'm sorry but I can't follow your steps. You appear to be solving but the steps are not apparent. If you have solved it correctly then (-3,-5,3) is NOT a solution. The signs of x and z are not correct.
In any case, you don't have to solve to answer the question. One equation is
x+4y+4z=-29
All you have to do is substitute
(-3)+4(-5)+4(3) ?=? -29
-3-20+12 ?=? -29
-11 ?=? -29
It is not equal so it is NOT a solution. If it were equal you should have two more equations in which you would try the proposed solution. Only if all three were equal would you be able to say it was a solution.

 

[Unco]

G'day, Milanna.

Given the system of equations:

\(\displaystyle \L \begin{align}x \, + \, 4y \, + \, 4z \, &= \, -29 \\
3y \, + \, 3z \, &= \, -24 \\
z \, &= \, -3 \\
\end{align*}\)

Determine if the given ordered triple (x, y, z) = (-3, -5, 3) is a solution to the system.

3y + 3z = -24
3y + 3(-3) = -24
3y -9 = -24
3y = -15
y=-5

x + 4y + 4z = -29
x + 4(-5) + 4(-3) = -29
x - 20 - 12 = -29
x - 32 = -29
x = 3

so I get x=3 y=-5 z=-3

Your solution is absolutely correct: (3, -5, -3). This is not the same as (-3, -5, 3) so their solution is incorrect.

Gene has shown how the question should be answered, but your work is fine nonetheless.

 

[Denis]

Don't think so Unco; problem states:
"determine if the given ordered triple is a solution of the system (-3, -5, 3) "

So answer is: "it is not" (she determined it is not)

 

[milanna]

I think where I made my mistake was in how I arranged my 3 solutions in the ordered triple.

I did not realize that an ordered triple needed to be in the form of (x, y, z).
I thought that the three solutions x, y, and z were interchangeable, if that makes any sense.
In my first post I arranged my ordered triple as (z, y, x) which corresponded to
(-3, -5, 3).
I actually should have arranged my ordered triple as (x, y, z), which would be (3, -5, -3).

So the answer is that the given ordered triple is NOT a solution of the system, correct?

 

[Unco]

An ordered triple is of the form (x, y, z) - like an ordered pair is of the form (x, y) - so, as I said earlier, you are correct.

 

[Gene]

It seems to be getting confused. to summerize. If you wanted to solve the system the steps I would use are
x+4y+4z = -29 1]
3y+3z = -24 2]
z = -3 3]
3y+3(-3)=-24 2]&3]
3y=-15
y=-5 4]
x+4(-5)+4(-3)=-29 1]&3]&4]
x=3

You solved it correctly. I was confused by the order.

As you corrected it in your last post the ordered triple of your solution is
(x,y,z) = (3,-5,-3)
The offered solution is
(x,y,z) = (-3,-5,3)

In your last post you said it is not the same so it is not a solution. Right, it is not.

I'm not saying anything new, just trying to put it all together.
If you didn't find the previous posts confusing, you may ignore this one.