DOK 2 Practice

Apply systems and inequalities to contexts, graphs, and constraints.

This set asks students to write models, interpret intersections, test feasible points, and choose efficient solving methods.

How to use this set

Use the structure of the problem: totals suggest equations, limits suggest inequalities, and isolated variables suggest substitution.

Home Math 1 Home Strand Page

Set Focus

Applied systems and constraints

DOK 2 questions usually require translating or switching representations before answering.

Contexts

Write systems from totals, prices, and equal-value situations.

Graphs

Read intersections and inequality shading.

Feasibility

Test ordered pairs against every constraint.

Strategy

Choose substitution or elimination based on equation structure.

Practice Questions

Applications and Representation Switching

Check your answer first, then reveal the explanation when you want the model.

Question 1

Write a system

A theater sells adult tickets for 8 dollars and student tickets for 5 dollars. Ten tickets cost 65 dollars total. Which system models the situation?

Question 2

Context solution

Using a+s=10 and 8a+5s=65, how many adult tickets were sold?

Question 3

Graph to solution

The lines y=x+2 and y=-2x+5 are graphed. What is their intersection point?

Two linear graphs

Question 4

Feasible point

A constraint is x+y\le12, with x\ge0 and y\ge0. Is (7,6) feasible?

Question 5

Inequality from context

A student can spend at most 40 dollars on notebooks that cost 4 dollars and binders that cost 6 dollars. Which inequality models the constraint?

Question 6

Graph an inequality

How should y\ge -x+4 be graphed?

Question 7

Interpret equal cost

Plan A costs 15+3m. Plan B costs 5+5m. For what value of m are the costs equal?

Question 8

Choose a strategy

Which first step is most efficient for solving 2x+3y=18 and x-3y=0?

Question 9

Parallel lines

What is the solution type for 3x+y=8 and y=-3x+2?

Question 10

Strict inequality

Which description matches y<x+1?

Back to Systems & Inequalities Back to Math 1