Question

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Answer 1

@Directrix

Answer 2

The object is to eliminate one of the three variables and reduce the system of equations to a 2 by 2 system. After that, the next task is to eliminate one of the remaining two variables.

Answer 3

OK

Answer 4

(1) x + y + z = -5
(2) x - y + 3z = -1
(3) 4x + y + z = -2

Answer 5

In equations 1 and 2, add the two equations. The y variables will add to 0.

x + y + z = -5
x - y + 3z = -1
-----------------
2x + 4z = -6 --->**

Answer 6

In equations 2 and 3, add the two equations. The y variables there will also add to 0.
(2) x - y + 3z = -1
(3) 4x + y + z = -2
-----------------------
5x + 4z = -3---> **

Answer 7

The variable y has been eliminated. Look back at the work and see if you understand how that was done.

Answer 8

OHHH

Answer 9

The 3 by 3 system has been transformed to a 2 by 2 system:

2x + 4z = -6 --->**
5x + 4z = -3---> **

Answer 10

Look at the z variables. They are both +4z.

To eliminate the z variables, multiply each member of one of the two equations by (-1).

Answer 11

MAKES SINCE SO FAR

Answer 12

2x + 4z = -6 ---> Mult by -1 -2x -4z = 6
5x + 4z = -3---> 5x + 4z = -3
---------------
3x = 3
x = 1

Answer 13

X has been found. Now, we have to find y and z.

Answer 14

OHHH

Answer 15

Using one of the 2 variable equations, substitute 1 in for x and solve for y.

2x + 4z = -6

2*1 + 4z = -6

2 + 4z = -6
-2 -2
---------------
4z = -8
z = -2

Answer 16

So, x = 1 and z = -2

Go to one of the 3 by 3 equations and substitute in for x and z.

Then, you can find y.

Answer 17

WOW I THOUGHT IT WAS LESS THEN THISS HAHA

Answer 18

I chose the first one.

(1) x + y + z = -5

1 + y -2 = -5

y -1 = -5

y = -5 + 1

y = -4

(1, -4, -2)

You should copy this so that you will have an example to use in similar problems.

Answer 19

HEY IM FIXEN TO GO TO BED WE WILL FINISH THIS TOMORROW PLZ

Answer 20

Also, check out this 3 by 3 online solver.

http://math.bd.psu.edu/~jpp4/finitemath/3x3solver.html

Answer 21

OK I WILL