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y≤13x−3 y≤−2x−2\begin{aligned} y &\leq \dfrac{1}{3}x-3 \ y &\leq -2x-2 \end{aligned}

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Q. y≤13x−3 y≤−2x−2\begin{aligned} y &\leq \dfrac{1}{3}x-3 \ y &\leq -2x-2 \end{aligned}
  1. Identify Inequalities System: Identify the system of inequalities that needs to be solved.\newlineThe system of inequalities given is:\newliney≤13x−3y≤−2x−2 \begin{aligned} y &\leq \dfrac{1}{3}x-3 \\ y &\leq -2x-2 \end{aligned}
  2. Graph First Inequality: Graph the first inequality y≤13x−3y \leq \dfrac{1}{3}x-3.\newlineTo graph this inequality, we would first graph the line y=13x−3y = \dfrac{1}{3}x-3 and then shade the area below the line since the inequality is y≤13x−3y \leq \dfrac{1}{3}x-3.
  3. Graph Second Inequality: Graph the second inequality y≤−2x−2y \leq -2x-2.\newlineSimilarly, we would graph the line y=−2x−2y = -2x-2 and then shade the area below this line because the inequality is y≤−2x−2y \leq -2x-2.
  4. Find Intersection of Areas: Find the intersection of the two shaded areas.\newlineThe solution to the system of inequalities is the region where the shaded areas from Step 22 and Step 33 overlap.
  5. Interpret Solution: Interpret the solution.\newlineThe overlapping region represents all the points (x,y)(x, y) that satisfy both inequalities. This is the solution to the system of inequalities.

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