The Following System Does Not Have a Unique Solution $$\left\{ \begin{array} { l } x + 4 y - 2 z = - 5 \\3 x - 6 y + 6 z = 7 \\5 x + 2 y + 2 z = - 3\end{array} \right.$$

question 81

Multiple Choice

The following system does not have a unique solution. Solve the system.
- $$\left\{ \begin{array} { l } x + 4 y - 2 z = - 5 \\3 x - 6 y + 6 z = 7 \\5 x + 2 y + 2 z = - 3\end{array} \right.$$

• A) infinitely many solutions of the form \(x = - \frac { 1 } { 9 } - \left( \frac { 2 } { 3 } \right) z , y = - \frac { 11 } { 9 } + \left( \frac { 2 } { 3 } \right) z , z = z\)
• B) inconsistent system, no solution
• C) \(x = 0 , y = 0 , z = \frac { 3 } { 2 }\)
• D) infinitely many solutions of the form \(x = \frac { 19 } { 3 } + \frac { 8 } { 9 } z , y = \frac { 5 } { 6 } - \frac { 13 } { 18 } z , z = z\)

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