Question

Solve for all variables. With explanation please.
x+2y+3z=24
-x+y-2z=1
x+y-2z=9

Answer 1

Typically, the phrase that would go with this is "3 equations and 3 unknowns --- Problem solved!"

Can you tell me what level of math you are working with? Linear Algebra or something else?

Answer 2

If you are not in Linear Algebra, then one method would look like this:

You are given:

(1) x + 2y + 3z = 24
(2) -x + y - 2z = 1
(3) x + y - 2z = 9

Step 1. Solve (3) for x and substitute the result into (1) and (2) creating a new (1) and new (2).
Step 2. Solve the new (2) for y and substitute the result into the new (1). The result will be an equation in terms of one variable (namely z). Solve for Z.

Then you would do the same, to solve for x and y.

Answer 3

\[\left\{x=4,y=\frac{55}{7},z=\frac{10}{7}\right\} \]

Answer 4

It algebra linear

Answer 5

From Mathematica 8:\[\text{LinearSolve}\left[\left( \begin{array}{ccc} 1 & 2 & 3 \\ -1 & 1 & -2 \\ 1 & 1 & -2 \end{array} \right),\left( \begin{array}{c} 24 \\ 1 \\ 9 \end{array} \right)\right]=\left\{4,\frac{55}{7},\frac{10}{7}\right\} \]

Answer 6

Thank u robtobey but the answer sheet has a different answer.

Answer 7

Attached is a Mathematica solution and verification of the results.