Questions: Graph the solution of the system of linear inequalities. y < -5x - 3 y > x + 6

Transcript text: Graph the solution of the system of linear inequalities. \[ \left\{\begin{array}{l} y<-5 x-3 \\ y>x+6 \end{array}\right. \]

Solution

Solution Steps

Step 1: Identify the inequalities

The given system of linear inequalities is: \[ \left\{\begin{array}{l} y < -5x - 3 \\ y > x + 6 \end{array}\right. \]

Step 2: Convert inequalities to equations for plotting

Convert the inequalities to equations for plotting the boundary lines:

$ y = -5x - 3 $
$ y = x + 6 $

Step 3: Determine the axis range

To ensure the graph captures the intersection and relevant regions, choose an appropriate range for $ x $ and $ y $. Let's use:

$ x $ range: $-10$ to $10$
$ y $ range: $-20$ to $20$

Final Answer

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -20, "ymax": 20}, "commands": ["y = -5x - 3", "y = x + 6"], "latex_expressions": ["$y = -5x - 3$", "$y = x + 6$"]}

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