MA.912.AR.9.6 · Linear Relationships

Constraints as Systems and Viable Solutions: Sample Algebra 1 EOC Questions

Real problems come with limits: a budget, a capacity, a number of hours. Students represent those limits as a system of equations or inequalities and then judge whether a proposed answer is actually viable, since a solution can be mathematically correct and still impossible in context.

How the Algebra 1 EOC tests this benchmark

Every item on this benchmark is real-world. Viability is the point: a solution of 4.5 buses or negative 3 tickets solves the algebra and fails the situation. Multiselect items asking which options are viable are common, alongside multiple choice items asking which system represents the constraints.

Skills students need

Write constraints as a system
Decide whether a solution is viable in context
Interpret non-negative and whole-number restrictions
Match a real-world limit to an inequality symbol

Try 6 real MA.912.AR.9.6 questions

These come straight from Algebro's Algebra 1 question bank, easiest first. Answer one, check it, then move to the next.

Question 1 of 6

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Question 1EasyMultiple Select

A garden bed holds at most 10 plants, so the constraint is

t + p \leq 10

, where

t

is the number of tomato plants and

p

is the number of pepper plants. Both counts must be whole numbers that are not negative. Select ALL ordered pairs

(t, p)

that are VIABLE solutions.

Select every answer that applies, then check.

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Question 6HardMatching

A flower shop bouquet holds at most 11 stems, so the constraint is

n + b \leq 11

, where

n

is the number of roses and

b

is the number of lilies. Both counts must be whole numbers that are not negative. Match each ordered pair to its verdict.

Pick one match in each row, then check.

	A.Viable	B.Non-viable
$(7, 6)$
$(5, 4)$
$(-1, 9)$
$(3, 8)$

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