Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.6

ALG2.58 Checking System Solutions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.58 Checking System Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.58 Checking System Solutions - Select the statement that correctly verifies candidate solutions by substitution and select the statement that explains why an inconsistent system has no solution. Associated source-listed standards: CCSS A-REI.6; MP.6; CA CCSSM A-REI.6; MP.6; MA 2017 A-REI.6; MP.6; NY NGLS A-REI.6; MP.6; TX TEKS Algebra II: §111.40.

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 II

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 ALG2.58 Checking System Solutions skill assessments:

Problem 1Difficulty: Mastery

When (-1/2, 4) is substituted into the system -5x + 6y = 53/2 and y = -1/5x + 4/5, how many equations are true? Enter a number.

Solution & Explanation:(-1/2, 4) makes 1 equation true, so the numeric answer is 1.

Problem 2Difficulty: Mastery

For the system x - y = 1/2 and -x + 2y = 0, Jalen and Priya make these claims about (-3, 2). Who is right? Jalen: "(-3, 2) is a solution because every checked pair works for one of the equations." Priya: "(-3, 2) is not a solution because it fails both equations."

ABoth students.

BPriya only.

CJalen only.

DNeither student.

Solution & Explanation:(-3, 2) does not satisfy either equation, so it cannot be a solution. Only Priya is correct.

Problem 3Difficulty: Mastery

For the system y = 3/2x - 11/2 and x - 4y = 7, (9, 1/2) is checked and rejected. Which statement best explains why that alone does not prove the system has no solution?

AThe conclusion is incorrect because rejecting (9, 1/2) only shows that this pair is not a solution; another pair could still solve the system.

BThe conclusion is correct because any first rejected pair proves the system has no solution.

CThe conclusion is correct because every system can be checked with only one ordered pair.

DThe conclusion is incorrect only if (9, 1/2) actually makes both equations true.

Solution & Explanation:Rejecting (9, 1/2) only tells you that this one ordered pair does not satisfy both equations. It does not prove that no solution exists.

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Frequently Asked Questions

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QIs this ALG2.58 Checking System Solutions 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 II Math students. It aligns with educational standard A-REI.6 (Select the statement that correctly verifies candidate solutions by substitution and select the statement that explains why an inconsistent system has no solution. Associated source-listed standards: CCSS A-REI.6; MP.6; CA CCSSM A-REI.6; MP.6; MA 2017 A-REI.6; MP.6; NY NGLS A-REI.6; MP.6; TX TEKS Algebra II: §111.40.).