Questions: Graph the system of inequalities. y > x^2 - 7 y <= x - 2

Transcript text: Graph the system of inequalities. \[ \left\{\begin{array}{l} y>x^{2}-7 \\ y \leq x-2 \end{array}\right. \]

Solution

Solution Steps

Step 1: Identify the inequalities

The given system of inequalities is:

$ y > x^2 - 7 $
$ y \leq x - 2 $

Step 2: Solve the first inequality

The first inequality is $ y > x^2 - 7 $. This represents the region above the parabola $ y = x^2 - 7 $.

Step 3: Solve the second inequality

The second inequality is $ y \leq x - 2 $. This represents the region below or on the line $ y = x - 2 $.

Final Answer

The solution to the system of inequalities is the region above the parabola $ y = x^2 - 7 $ and below or on the line $ y = x - 2 $.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = x^2 - 7", "y = x - 2"], "latex_expressions": ["$y = x^2 - 7$", "$y = x - 2$"]}

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