Determine Whether the Two Systems of Linear Equations Yield the Same

question 39

Multiple Choice

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
$\left\{ \begin{aligned} x + y - 9 z & = - 67 \\ y + 5 z & = 31 \\ z & = 7 \end{aligned} \right.$
$\left\{ \begin{aligned} x - 9 y + 6 z & = 76 \\ y - 9 z & = - 67 \\ z & = 7 \end{aligned} \right.$

• A) \(x = 0 , y = - 4 , z = 7\)
• B) \(x = 0 , y = 4 , z = 7\)
• C) \(x = 4 , y = 7 , z = 0\)
• D) \(x = - 4 , y = 7 , z = 0\)
• E) The systems yield different solutions.

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Definitions:

Operant Conditioning

An educational technique that influences the strength of a behavior by awarding reinforcements or imposing penalties.

Operant Conditioning

An approach to teaching that relies on using incentives and penalties for actions, focusing on how outcomes affect actions.

Classical Conditioning

Learning by the method of associating an environmental stimulus with one that happens naturally.

Shaping

A method of teaching new behaviors through the use of reinforcement of successive approximations toward a desired behavior.