Question

Galena is solving the following system.

3x+2y+3z=5 (1)
7x+y+7z=-1 (2)
4x-4y-z=-1 (3)

Step 1: She multiplies equation (3) by 3 and adds it to equation (1).
Step 2: She multiplies equation (3) by –7 and adds it to equation (2).

Which statement explains Galena’s mistake?
She added equation (1) instead of equation (2) in step 1.
She did not multiply equation (3) in step 1 by the correct value.
She did not multiply equation (3) in step 2 by the correct value.
She added equation (2) instead of equation (1) in step 2.

Answer 1

can you check the problem, is that -2z in the third equation, ?and 72z in the second maybe

Answer 2

yeah sorry

Answer 3

okay I fixed it

Answer 4

ok, the point of this is to get a new equation that is less variables than before... so adding multiples of equations together should make one variable go to zero..

Answer 5

3x+2y+3z=5
7x+y+7z=-1
4x-4y-z=-1
----------------

3 times equation 3 then added to equation 1...
12x - 12y - 3z = -3

see how you get -3z, when added to equation 1, the z will go away, 3z + (-3z) = 0

3 times equation 3

3x+2y+3z=5
7x+y+7z=-1
12x-12y-3z=-3
---------------

added to equation 1
15x -10y = 2
7x+y+7z=-1
12x-12y-3z=-3
--------------

equation 1 now is less one variable...

Answer 6

This time it says, -7 times the third one then added to the second one
-7 times row 3 gives
3x+2y+3z=5
7x+y+7z=-1
-28x+28y+7z=7
---------------

adding that to equation 2 gives a new equation 2
3x+2y+3z=5
-21x+29y+14z=6
-28x+28y+7z=7
---------------

notice it did not reduce the variables doing that

Answer 7

you see all this?

Answer 8

yeah thank you