# Reasoning with Equations and Inequalities

Directions: Directions: Using the integers from −9 to 9 at most once each, place one in each box to create a system of equations as well as two solutions that make the system true. Source: Cody Pritchard

## Radical And Linear Function Intersection

Directions: Using the digits 1 to 9 at most one time each, to make one set of functions intersect exactly twice, one set of functions intersect exactly once, and one set of functions never intersect. Source: Mike Fouchet

## Parabola’s Vertex

Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create a correct sentence: The vertex of the parabola, y = ▢ x² + ▢ x + ▢, lies on the horizontal axis Source: Cecilia Calvo

## Infinitely Many Solutions System of Equations

Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create a a system of equations with infinitely many solutions. Source: Mike

Directions: Use only the digits 1-9, each digit only once, create a problem that has the solutions x = 4 and x = -1/2. Source: Amy Herzog

## Systems of Inequalities 2

Directions: Using the integers −9 to 9 at most one time each, place an integer in each box to create a system of inequalities as well as an included and excluded point. Make the points as close together as possible. Source: Robert Kaplinsky

## Systems of Inequalities 1

Directions: Using the integers −9 to 9 at most one time each, place an integer in each box to create a system of inequalities as well as an included and excluded point. Source: Robert Kaplinsky

## Systems of Equations 4

Directions: Using the integers −9 to 9 at most one time each, place an integer in each box to create a system of equations whose solution is as close to the origin as possible. Source: Robert Kaplinsky