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NY Regents Algebra I Systems of Linear Equations — practice questions — page 2

Explore 36 free Systems of Linear Equations questions in NY Regents Algebra I Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Systems of Linear Equations questions and exercises with answers

Showing questions 31–36 of 36.

The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length and width.Read the answer and worked solution →What do the lines doRead the answer and worked solution →One word is wrongRead the answer and worked solution →Complete the classificationRead the answer and worked solution →Which ones belongRead the answer and worked solution →Order the substitution stepsRead the answer and worked solution →

Worked practice questions

The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length and width.

  1. Length 8 and width 12
  2. Length 10 and width 10
  3. Length 12 and width 8
  4. Length 14 and width 6
Show answer and solution

Correct answer: C. Length 12 and width 8

1. Let L be the length and W be the width, giving the system 2L + 2W = 40 and L = W + 4. 2. Substitute W + 4 for L in the perimeter equation: 2(W plus 4) plus 2W equals 40. 3. Distribute and simplify: 2W plus 8 plus 2W equals 40, so 4W equals 32, giving W equals 8. 4. Substitute W = 8 into L = W + 4 to get L equals 12, and checking confirms 2(12) plus 2(8) equals 40. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.4 Solve Applications with Systems of Equations_

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What do the lines do

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Items
  1. Item
    One solution
    Category
    Intersecting
  2. Item
    Lines cross once
    Category
    Intersecting
  3. Item
    Slopes differ
    Category
    Intersecting
  4. Item
    No solution
    Category
    Parallel
  5. Item
    Same slope only
    Category
    Parallel
  6. Item
    Infinite answers
    Category
    Coincident
  7. Item
    One line twice
    Category
    Coincident
Categories
  1. Item
    Intersecting
  2. Item
    Parallel
  3. Item
    Coincident
Instructions
Tap each fact into the picture of the graph it belongs to.
_Source: OpenStax Elementary Algebra 2e (CC BY 4.0), Ch 5 'Systems of Linear Equations', sections 5.1-5.3_

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One word is wrong

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Questions
  1. Statement parts
    1. A
    2. system
    3. with
    4. no
    5. solution
    6. is
    7. consistent
    Correction
    inconsistent
    Incorrect part
    consistent
  2. Statement parts
    1. Parallel
    2. lines
    3. give
    4. one
    5. solution
    Correction
    no
    Incorrect part
    one
  3. Statement parts
    1. Coincident
    2. lines
    3. give
    4. two
    5. solutions
    Correction
    infinitely many
    Incorrect part
    two
  4. Statement parts
    1. Elimination
    2. needs
    3. coefficients
    4. that
    5. are
    6. equal
    Correction
    opposites
    Incorrect part
    equal
Instructions
Tap the single word that makes the sentence false.
_Source: OpenStax Elementary Algebra 2e (CC BY 4.0), Ch 5 'Systems of Linear Equations', sections 5.1-5.3_

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