Free Printable WorksheetMathAlgebra IMath CurriculumA-REI.5–6

ALG1.57 Systems by Substitution Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.57 Systems by Substitution. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.57 Systems by Substitution - Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.5–6. Skill statement in this prompt cell: Select the correct solution to systems of two linear equations using substitution; Select the statement that correctly interprets the solution as an ordered pair that satisfies both equations. Associated standards listed with this skill in this prompt cell: CCSS: A-REI.5–6, 11; A-CED.3; TEKS: §111.39(c)(3)(C), (4)(C); VA SOL: A.EI.2 a–c, h; FL B.E.S.T.: MA.912.AR.9.1, 9.6; NY-NGLS: AI-A.REI.6, AI-A.REI.11; CA CCSSM: A-REI.6,11; MA 2017: HS.A-REI.6,11; DoDEA CCRSM; NAEP: Algebra—systems; NCTM P2A: Practices 1, 3.. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG1.57 Systems by Substitution skill assessments:

Problem 1Difficulty: Mastery
Two custom-shirt companies are modeled by y = 7x + 40 and y = 9x + 10. Let x represent shirts ordered and y represent total cost in dollars. The system is y = 7x + 40 and y = 9x + 10. Which statement correctly interprets the solution?
AThe solution is (145, 15), so both companies cost $15 for 145 shirts.
BThe solution is (15, 40), so both companies cost $40 for 15 shirts.
CThe solution is (7, 9), so both companies cost $9 for 7 shirts.
DThe solution is (15, 145), so both companies cost $145 for 15 shirts.
Solution & Explanation:Set the two cost equations equal: 7x + 40 = 9x + 10. Solving gives x = 15, and y = 145.
Problem 2Difficulty: Mastery
Two water tanks are modeled by y = 50 - 3x and y = 20 + 2x. Let x represent minutes and y represent gallons of water. The system is y = 50 - 3x and y = 20 + 2x. Which statement correctly interprets the solution?
AThe solution is (32, 6), so both tanks have 6 gallons after 32 minutes.
BThe solution is (6, 50), so both tanks have 50 gallons after 6 minutes.
CThe solution is (6, 32), so both tanks have 32 gallons after 6 minutes.
DThe solution is (3, 2), so both tanks have 2 gallons after 3 minutes.
Solution & Explanation:Set 50 - 3x equal to 20 + 2x. Solving gives x = 6, then y = 32.
Problem 3Difficulty: Mastery
Two phone plans are modeled by y = 0.10x + 30 and y = 0.05x + 45. Let x represent minutes and y represent total cost in dollars. The system is y = 0.10x + 30 and y = 0.05x + 45. Which statement correctly interprets the solution?
AThe solution is (60, 300), so both phone plans cost $300 at 60 minutes.
BThe solution is (300, 60), so both phone plans cost $60 at 300 minutes.
CThe solution is (300, 30), so both phone plans cost $30 at 300 minutes.
DThe solution is (0.10, 0.05), so both phone plans cost $0.05 at 0.10 minutes.
Solution & Explanation:Set 0.10x + 30 equal to 0.05x + 45. Solving gives x = 300, and y = 60.

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Frequently Asked Questions

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QIs this ALG1.57 Systems by Substitution worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-REI.5–6 (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.5–6. Skill statement in this prompt cell: Select the correct solution to systems of two linear equations using substitution; Select the statement that correctly interprets the solution as an ordered pair that satisfies both equations. Associated standards listed with this skill in this prompt cell: CCSS: A-REI.5–6, 11; A-CED.3; TEKS: §111.39(c)(3)(C), (4)(C); VA SOL: A.EI.2 a–c, h; FL B.E.S.T.: MA.912.AR.9.1, 9.6; NY-NGLS: AI-A.REI.6, AI-A.REI.11; CA CCSSM: A-REI.6,11; MA 2017: HS.A-REI.6,11; DoDEA CCRSM; NAEP: Algebra—systems; NCTM P2A: Practices 1, 3.. Use this prompt-provided wording as the supporting standard description for this workflow.).

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