Question

If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable z is eliminated in the first and second equations, then the second and third equations.
x - 3y - 3z = -13
x + 2y - z = -1
2x + 3y + 2z = 0

A) x - 3y = -13
-2x - 9y = -10
B) 2x + 3y = 0
4x + 7y = -2
C) -2x - 9y = -10
4x + 7y = -2
D) x - 3y = -13
2x + 3y = 0

Answer 1

It's C. Do you have any idea how to find this out and what to do to get it?

Answer 2

I have no idea /: could you help me please? @IMStuck

Answer 3

I would be honored...The first two equations are as such (we only work with 2 at a time here, ok?)
x - 3y - 3z = -13
x + 2y - z = -1

Answer 4

Between these 2 your goal is to eliminate the z's. In order to do that, you have to make their coefficients the same, one positive and one negative, so that when you add them together, they equal 0. Like this:

Answer 5

In order to make the -z in the second equation become a +3z (the 3 is from the first equation's z coefficient, and the + is sign opposite what is in front of the 3z in the first equation), you have to multiply it by a -3. Watch...

Answer 6

-3(x + 2y - z = -1)--> -3x - 6y + 3z = 3. See? This is the "new"second equation. Now we will add to the first equation and watch what happens:

Answer 7

x - 3y - 3z = -13
-3x - 6y + 3z = 3
----------------
-2x - 9y + 0z = -10
Of course a 0z is nothing, so the new equation between the first two, eliminating the z, is
-2x - 9y = -10

Answer 8

Now we will do the same with the second 2 equations here.

Answer 9

you know I'm actually understanding everything you're saying this is great

Answer 10

They are:
x + 2y - z = -1
2x + 3y + 2z = 0

Answer 11

In order to eliminate the z's between the second 2 equation, we again have to make the coefficients the same, one with a negative sign, the other with a positive sign, so they cancel like they did in the first 2 equations. In order to get the coefficients in front of the z's to be the same, we have to multiply the second equation by a 2. Watch...

Answer 12

2( x + 2y - z = -1) --> 2x + 4y - 2z = -2

Answer 13

Now we add that to the third equation to get:

Answer 14

2x + 4y - 2z = -2
2x + 3y + 2z = 0
----------------
4x + 7y + 0z = -2
Of course, again, 0z is nothing so the answer, having eliminated the z between the second and third equations, is
4x + 7y = -2

Answer 15

Do you see those two choices above? They will be:
-2x - 9y = -10
4x + 7y = -2

Answer 16

yes yes yes and i understand thank you so so much !!! @IMStuck

Answer 17

You are more than welcome, my dear!