IMG_0375.jpeg

# TEK 2A.3F ## Solve the systems of inequalities **Problem 31:** * $x + 2y ≤ 8$ * $3x - y > 5$ * $-y \ge -x + 3$ * $2x + y < 7$ * $x-y ≥ 3$ * $x-2y ≥ 1$ ## Graphs: The image shows two coordinate planes. Each plane displays a system of inequalities graphed in various colors and styles. Some li...

# TEK 2A.3F ## Solve the systems of inequalities **Problem 31:** * $x + 2y ≤ 8$ * $3x - y > 5$ * $-y \ge -x + 3$ * $2x + y < 7$ * $x-y ≥ 3$ * $x-2y ≥ 1$ ## Graphs: The image shows two coordinate planes. Each plane displays a system of inequalities graphed in various colors and styles. Some lines are solid, while others are dashed, indicating whether the inequality includes or excludes the line itself. Arrows extending outward from the lines indicate the regions satisfying the inequalities. Shading indicates the intersection zone where all the inequalities in a graph are satisfied. # TEK 2A.63B ## Solve the system of 3 linear equations with 3 variables **Problem 34:** A bakery sells three types of cookies: chocolate chip (C), oatmeal raisin (O), and peanut butter (P). A total of 240 cookies were sold. * The number of chocolate chip cookies sold (C) was twice the number of oatmeal raisin cookies sold (O). * The number of peanut butter cookies sold (P) was 20 more than the number of oatmeal raisin cookies (O). **Problem 35:** * $2x + y - z = 8$ * $-3x - y + 2z = -11$ * $-2x + y + 2z = -3$ **Problem 36:** * $x + y + z = 6$ * $2x + 3y + z = 14$ * $x + 2y + z = 10$ ## Solutions for Problem 34 (Bakery Cookies): * **Chocolate Chip (C):** 110 * **Oatmeal Raisin (O):** 55 * **Peanut Butter (P):** 75 ## Solutions steps (Problem 34 - 36) The image shows the steps taken to solve the system of equations and linear inequalities. Calculations, substitutions and algebraic manipulations are shown for each problem set.