Questions: Decide whether or not the ordered pair (-6,-6) is a solution of the system: 3x+y=-12 2x+3y=6 Select one: A. No B. Yes

Transcript text: Decide whether or not the ordered pair $(-6,-6)$ is a solution of the system: \[ \begin{array}{l} 3 x+y=-12 \\ 2 x+3 y=6 \end{array} \] Select one: A. No B. Yes

Solution

Solution Steps

To determine if the ordered pair $(-6, -6)$ is a solution to the system of equations, substitute $x = -6$ and $y = -6$ into both equations. Check if both equations are satisfied with these values. If both equations hold true, then the ordered pair is a solution; otherwise, it is not.

Step 1: Substitute the Ordered Pair into the First Equation

Substitute $x = -6$ and $y = -6$ into the first equation $3x + y = -12$:

\[ 3(-6) + (-6) = -18 - 6 = -24 \]

Since $-24 \neq -12$, the ordered pair $(-6, -6)$ does not satisfy the first equation.

Step 2: Substitute the Ordered Pair into the Second Equation

Substitute $x = -6$ and $y = -6$ into the second equation $2x + 3y = 6$:

\[ 2(-6) + 3(-6) = -12 - 18 = -30 \]

Since $-30 \neq 6$, the ordered pair $(-6, -6)$ does not satisfy the second equation.

Final Answer

Since the ordered pair $(-6, -6)$ does not satisfy either of the equations, it is not a solution to the system. Therefore, the answer is $\boxed{\text{A. No}}$.

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