Questions: Graph the given system of linear inequalities. 3x + y ≥ -6 3x + y ≥ 6 Use the graphing tool to graph the system.

Transcript text: Graph the given system of linear inequalities. \[ \left\{\begin{array}{l} 3 x+y \geq-6 \\ 3 x+y \geq 6 \end{array}\right. \] Use the graphing tool to graph the system. $\square$

Solution

Solution Steps

Step 1: Solve the first inequality

The first inequality is:

\[ 3x + y \geq -6 \]

To find the boundary line, we set the inequality to equality:

\[ 3x + y = -6 \]

Solving for $y$, we get:

\[ y = -3x - 6 \]

Step 2: Solve the second inequality

The second inequality is:

\[ 3x + y \geq 6 \]

To find the boundary line, we set the inequality to equality:

\[ 3x + y = 6 \]

Solving for $y$, we get:

\[ y = -3x + 6 \]

Final Answer

The system of inequalities is represented by the lines $y = -3x - 6$ and $y = -3x + 6$. The solution region is the area where both inequalities are satisfied.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = -3x - 6", "y = -3x + 6"], "latex_expressions": ["$y = -3x - 6$", "$y = -3x + 6$"]}

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