Question

Explain, in complete sentences, which method you would use to solve the following system of equations and why you chose that method. Provide the solution to the system.

x - 3y + 2z = -12
x + 2y + 3z = 6
2x - 3y - z = -2

Answer 1

@teacherman79 @thomaster @TSwizzle @e.mccormick

Answer 2

which method would you use?

Answer 3

I don't know, I have been having trouble understanding how to complete these types of questions.

Answer 4

@teacherman79

Answer 5

The main methods are graphing, elimination, and substitution. This leads to an overview of them all:
http://www.purplemath.com/modules/systlin1.htm

Answer 6

Elimination. Can you help me solve it? @e.mccormick

Answer 7

OK, for elimination you add multiples of one equation to another with the goal of eliminating variables until you have solutions to use.

Answer 8

Lets start by labeling these equations.
\(~\bbox[3px,border:2px solid red]{1}~x - 3y + 2z = -12 \)
\(~\bbox[3px,border:2px solid red]{2}~x + 2y + 3z = 6 \)
\(~\bbox[3px,border:2px solid red]{3}~2x - 3y - z = -2 \)

Now, if I take Equation 1 (Eq1) and multiply it by -1 and then add it to Eq2, what do I get?

Answer 9

\(\begin{array}
\.-1 \times & x - 3y + 2z = -12 \\
+ & x + 2y + 3z = 6
\end{array}\)
becomes
\(\begin{array}
~& -x + 3y - 2z = 12 \\
+ & \;\;\: x + 2y + 3z = 6
\end{array}\)
which means:
\( x-x + 2y + 3y + 3z - 2z = 6+ 12\)
which simplifies to
\( 5y + z = 18 \)

As you can seem this eliminates the x. That is why they call it elimination.

You need to eliminate another x in another equation. Then you can use the two new ones, call them Eq4 and Eq5 to eliminate either a y or a z. Then you will have one of the answers.