Find the Solution or Solutions, If Any Exist, to the System

question 70

Multiple Choice

Find the solution or solutions, if any exist, to the system.
- $$\left\{ \begin{array} { c } 2 x - 6 z - 6 w = - 4 \\x + y + z + 3 w = 2 \\4 x + 2 y - 4 z - 4 w = 0 \\6 x + 4 y - 2 z + 2 w = 4\end{array} \right.$$

• A) infinitely many solutions of the form \(x = 3 z - 2 , y = - 4 z + 4 , z = z , w = 0\)
• B) inconsistent system, no solution
• C) \(x = - 2 , y = 4 , z = 0 , w = 0\)
• D) infinitely many solutions of the form \(x = - 3 z - 2 , y = 4 z + 4 , z = 0 , w = w\)

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Definitions:

Workable Goal

A realistic and achievable objective, often set in therapeutic, personal, or professional contexts to ensure progress and success.

Past-Exception Question

A question used in therapy to help clients identify times in the past when their problem did not occur, emphasizing their ability to overcome difficulties.

Miracle Question

A solution-focused technique that asks clients to envision how their life would change if a miracle solved their biggest problem overnight.

Double-Sided Reflection

In motivational interviewing, a technique that acknowledges what a client has said but also introduces an alternative perspective to consider.