Question

Can somebody please help me with elimination?
Please show and explain your work.
-2x+2y+3z=0
=2x-y+z=-3
2x+3y+3z=5 "
I like to work along with you, step by step. If you could please allow a few seconds for me to write the work down as we go. I like to learn, NO giving answers. Will medal/fan as always.

Answer 1

In general, we consider a subsystem composed by two equations. For example, we can consider the subsystem composed by the first two equations:
\[\left\{ \begin{gathered}
- 2x + 2y + 3z = 0 \hfill \\
- 2x - y + z = - 3 \hfill \\
\end{gathered} \right.\]

Answer 2

is the 2nd one a neg or pos 2x ??

Answer 3

Negative.

Answer 4

Now I rewrite my system above like this:
\[\left\{ \begin{gathered}
- 2x + 2y = - 3z \hfill \\
- 2x - y = - 3 - z \hfill \\
\end{gathered} \right.\]
As we can consider it, like a system of two unknowns \(x,y\), so, we can solve it with respect to \(x,y\) as functions of the third unknown \(z\)
please try

Answer 5

oops.. As we can see , we can consider it...

Answer 6

\[ \begin{array}l\color{red}{\text{ }}\color{orange}{\text{ }}\color{#E6E600}{\text{}}\end{array} \]

Answer 7

I'm not really sure what you mean.

Answer 8

do you know how to solve a linear system of two equations and two unknowns?

Answer 9

hint:
we have to solve the system above, supposing that the third unknown, is known
so, we have to solve that system for \(x,y\). After that, you should get the values of \(x\) and \(y\) as a functions of \(z\)