Question

can someone show me step by step how to do this?
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 + y – 3z = –8
2x + 2y + z = 12
3x + y – z = –2

Answer 1

ok, well you have

x + y – 3z = –8
2x + 2y + z = 12
3x + y – z = –2

so, the idea is that you will pick a "pair" of equations firstly from there
eliminate ONE variable, say "z"
and you'd get a 1ST NEWLY FORMED EQUATION with only "x" and "y"

so, you go back to the 3 equations and pick "another pair", and eliminate "z" again
and you'd get a 2ND NEWLY FORMED EQUATION with only "x" and "y"

so, now you'd end up with 2 NEW EQUATIONS with only "x" and "y"
and you work those like any 2x2 system of equations :)

Answer 2

gsheila27 confused?

Answer 3

kind of. if u were to do it step by step i would understand it better @jdoe0001

Answer 4

ok

Answer 5

$$
\begin{matrix}
x &+ y &– 3z &= –8\\
2x &+ 2y &+ z &= 12\\
3x &+ y &– z &= –2 \\
\end{matrix}\\
\color{blue}{\text{so, let's take the 1st and 2nd}}\\
---------------------\\
\begin{matrix}
x &+ y &– 3z &= –8 \\
2x &+ 2y &+ z &= 12& \times 3\\
\end{matrix}\\
----------------------\\
\begin{matrix}
x &+ y &– 3z &= –8\\
6x &+ 6y &+ 3z &= 36 & \times 3\\
\hline \\
7x& +7y & +0 &= 28
\end{matrix}

$$

Answer 6

so you end up with 1st NEW EQUATION

Answer 7

ohk :)
@jdoe0001

Answer 8

$$
\begin{matrix}
x &+ y &– 3z &= –8\\
2x &+ 2y &+ z &= 12\\
3x &+ y &– z &= –2 \\
\end{matrix}\\
\color{blue}{\text{so, let's take the 1st and 3rd}}\\
---------------------\\
\begin{matrix}
x &+ y &– 3z &= –8\\
3x &+ y &– z &= –2 & \times -3\\
\end{matrix}\\
----------------------\\
\begin{matrix}
2x &+ y &– 3z &= –8\\
-9x &-3y &+3z &= 6 & \times -3\\
\hline \\
-7x& -2y & +0 & = -2
\end{matrix}
$$

Answer 9

so , now you have the 2nd NEW EQUATION

Answer 10

now you just use the NEW EQUATIONS with only "x" and "y"
solve by elimination for either :)
so, you'll get one and the other
grab both and plug them on any of the 3 equations, and solve for "z"

Answer 11

so i would use the -7x -2y etc..... with the last equation ? @jdoe0001

Answer 12

you'd use the 2 NEW EQUATIONS, which do not contain "z"
just "x" and "y"

so they're just a system of 2 variables

Answer 13

so you'd solve say

7x +7y = 28
-7x -26 =-2

Answer 14

if you add them up, right off, "x" drops off, so, that came up quite simple

Answer 15

ty so much

Answer 16

yw