Question

how do you solve -x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20....it's 3 equations by elimination

Answer 1

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-x-5y-5z=2
4x-5y+4z=19
x+5y-z=-2


The first step is to use the elimination method to solve the first two equations. Basically, you'll solve it like it's a normal system of equations by solving the first two:

So,

-x - 5y - 5z = 2
4x - 5y + 4z = 19

Solve this like a normal system and then we can move on. (TIP: Eliminate x)

Answer 2

3x-z=21

Answer 3

did i do that right?

Answer 4

-x -5y -5z = 2
4x - 5y + 4z = 19

Multiply by 4.

-4x -20y - 20z = 8
4x - 5y + 4z = 19
-25y - 16z = 27

-25y = -16z + 27

\[y = \frac{ 25 }{ 16}z + -\frac{ 25}{ 27}\]

Answer 5

wouldn't it be 16/25 ?

Answer 6

Now, remember our goal is NOT to solve, so the above answer that I provided is WRONG. We want to add the first two systems together.

NOT SOLVE! (I solved it to show you the correct way, even though we won't use it.)

-x -5y -5z = 2
4x - 5y + 4z = 19


Upon adding

3x - 10y - 1z = 21

Second we subtract the third equation from the second in order to get another equation with two variables. Now we have a system of two equations with two variables:

3x - 10y - 1z = 21
x+5y-z=-2

Can you subtract these two systems? Notice, the -z and -1z will cancel out, creating a two variable system.

Answer 7

4x-5y=19

Answer 8

Good!

Start by adding the first and third equations and solving for z:
(-x - 5y - 5z) + (x + 5y - z) = 2 + (-2)
-6z = 0
z = 0

Plug that back into the first equation and solve for x:
-x - 5y - 5z = 2
-x - 5y - 5(0) = 2
-x - 5y = 2
x + 2 = -5y
x = -5y - 2

Now plug in -5y-2 for x and 0 for z in the second equation and solve for y:
4x - 5y + 4z = 19
4(-5y - 2) - 5y + 4(0) = 19
-20y - 8 - 5y = 19
-25y - 8 = 19
-25y = 27
y = -27/25

Finally, plug y=-27/25 and z=0 into the third equation and solve for x:
x + 5y - z = -2
x + 5(-27/25) - 0 = -2
x - 27/5 = -2
x = 27/5 - 2
x = 17/5

So, the solution is x = 17/5, y = -27/25, z = 0. Hope that helps! :)

Answer 9

according to the book the answers are (-2, -3, 3) though... so i am stilll a little bit confused on that part

Answer 10

You need to verify what it's asking for. I solved all the systems how they should be solved.

Answer 11

i think there is aproblem with the question, i will ask my teacher tomorrow... thanks for the help though :)

Answer 12

You're welcome! Maybe it was asking something different, and by, "solve," it was discussing something you learned in class.

Answer 13

maybe we have a sub for the next 3 months, so it's kind of confusing

Answer 14

i) There are various methods of solving these type of equations; such as elimination, Kramer's rule, matrix method etc. You have not specified which method is required; so let me solve the same by elimination method.

ii) Here one of the variable is eliminated by taking pairs of equations, then it is solved. Here we will eliminate the variable y.

iii) Operating (2) - (1):
(4x - 5y + 4z) - (-x - 5y - 5z) = 19 - 2
==> 5x + 9z = 17 ------- (4)

iv) Add (1) & (3): -6z = 0; ==> z = 0
Plugging z = 0, in the above (4) and solving x = 17/5

Sub. x = 17/5 and z = 0 in (1): -17/5 - 5y - 0 = 2
==> 5y = -17/5 - 2 = -27/5
Solving y = -27/25

Thus, (x, y, z) = (17/5, -27/25, 0)

Answer 15

yes i totally understand how you got that answer... the question must have had a typo

Answer 16

Must be... Hmm... You'll need to ask your teacher. This is most likely a typo.