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Reasoning with Equations and Inequalities

Create a System of Two Equations

Directions: Use non-zero whole numbers 1 to 30, at most once time each, to create a system of two linear equations where (3, 2) is the solution to the system. Source: Daniel Luevanos

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Linear Inequalities in Two Variables

Directions: Create 5 ordered pairs using the whole digits 0 – 9 exactly one time each. Then, create a linear inequality such that: 1. Two of the ordered pairs are solutions to the linear inequality. 2. Two of the ordered pairs are not solutions to the linear inequality. 3. One of the ordered pairs is on the boundary line but …

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System of Inequalities 2

Directions: Fill each blank with a different integer such that the point (4,4) is in the region created by the constraints has the least amount of area. Source: Erick Lee

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System of Inequalities

Directions: Fill each blank with a different integer such that the point (4,4) is within the solution region created by the constraints. Source: Erick Lee

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Finding the Length of a Right Triangle’s Altitude

Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment. Source: Kate Nerdypoo

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