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Grade 9 · Math · Algebra 1

9th grade Systems: one, none or infinitely many solutions, and the quickest method worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Systems: one, none or infinitely many solutions, and the quickest method

Grade 9 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Read this first

    Use this

    Rule A starts at 5 and steps up 2 each row. Rule B starts at -3 and steps up 2 each row.

  2. Ari writes two rules on a sticky note: y = 2x + 5 and y = 2x - 3. How many solutions does the system have?

    • One solution (independent)
    • No solution (inconsistent)
    • Infinitely many solutions (dependent)

  3. Use this

    Rule A starts at 6 and steps down 2 each row. Rule B starts at 6 and steps down 2 each row.

  4. Jun sketches two rules for a board game: y = -2x + 6 and y = 6 - 2x. How many solutions does the system have?

    • Infinitely many solutions (dependent)
    • One solution (independent)
    • No solution (inconsistent), because the two lines look parallel

  5. Use this

    Rule A starts at 2 and steps up 1 each row. Rule B starts at -4 and steps up 3 each row.

  6. Kira draws two rules on graph paper: y = x + 2 and y = 3x - 4. How many solutions does the system have?

    • One solution (independent)
    • No solution (inconsistent)
    • Infinitely many solutions (dependent)

  7. Use this

    Rule A starts at 8 and steps down 2 each row. Rule B starts at -1 and steps up 1 each row.

  8. Luz tests two rules from a puzzle book: y = -2x + 8 and y = x - 1. How many solutions does the system have?

    • No solution (inconsistent)
    • Infinitely many solutions (dependent)
    • One solution (independent)

  9. Table A (x | y)

    0 | 4; 1 | 7; 2 | 10; 3 | 13. Table B (x | y): 0 | 10; 1 | 13; 2 | 16; 3 | 19.

  10. Milo measures two plants in a table. Both tables follow steady rules. How many solutions does the system have?

    • No solution (inconsistent)
    • Infinitely many solutions (dependent)
    • One solution (independent)

  11. Table A (x | y)

    0 | 2; 1 | 7; 2 | 12; 3 | 17. Table B (x | y): 0 | 2; 1 | 7; 2 | 12; 3 | 17.

  12. Pia times two race turtles in a table. Both tables follow steady rules. How many solutions does the system have?

    • Infinitely many solutions (dependent)
    • One solution (independent)
    • No solution (inconsistent), since the two tables look different

  13. Table A (x | y)

    0 | 11; 1 | 7; 2 | 3; 3 | -1. Table B (x | y): 0 | 11; 1 | 7; 2 | 3; 3 | -1.

  14. Ren fills two buckets and logs a table. Both tables follow steady rules. How many solutions does the system have?

    • Infinitely many solutions (dependent)
    • No solution (inconsistent)
    • One solution (independent)

  15. 3x + 2y = 16. Equation 2: 5x - 2y = 8. Tala stacks 3x + 2y = 16 over 5x - 2y = 8. Which letter disappears when the two equations are added?

    • Only x disappears
    • Neither letter disappears
    • Only y disappears

  16. 4x + 3y = 17. Equation 2: 4x + y = 11. Zee stacks 4x + 3y = 17 over 4x + y = 11. Which letter disappears when the two equations are added?

    • Neither letter disappears
    • Only x disappears, because the x-numbers match
    • Only y disappears

  17. 5x + 2y = 19. Equation 2: 5x + 3y = 24. Bo stacks 5x + 2y = 19 over 5x + 3y = 24. Which letter disappears when the two equations are added?

    • Only y disappears
    • Only x disappears
    • Neither letter disappears
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9th grade Systems: one, none or infinitely many solutions, and the quickest method worksheet – printable
Print: 123456

About this worksheet

Systems: how many solutions, and the quickest method. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can tell, without graphing, whether a system has one solution, no solution or infinitely many, by comparing the step and the start of each rule.
  • I can rewrite an equation to y = mx + b, or compare ax + by = c pairs, and choose the first step that makes a letter disappear.
  • I can find the number that makes a system have no solution, and I know a solution stays the same when one equation is replaced by the sum of two.

Standard: A-REI.C.5, A-REI.C.6

Words to know

system: Two equations about the same x and y.

independent: Different steps: the lines cross once, so one solution.

inconsistent: Same step, different starts: the lines never meet, so no solution.

dependent: Same step and same start: one line twice, so infinitely many solutions.

step / start: The step is how much y changes for 1 more x; the start is y when x is 0.

eliminate: Add or subtract equations so one letter disappears.

Common mistakes

Your child expected two lines to cross once, even though the steps match.

Your child saw two equally steep lines and called them the same line.

Your child said two matching rules never meet, but they are the same line.

What to say

Ask: if two lines climb at the same rate, can the gap between them ever shrink?

Ask: do the two rules start at the same height?

Ask: do the rules give the same y for x = 0 and for x = 1?

Questions parents ask

What is the most common mistake with systems: one, none or infinitely many solutions, and the quickest method?

Your child expected two lines to cross once, even though the steps match.

How can I help my child with systems: one, none or infinitely many solutions, and the quickest method?

Ask: if two lines climb at the same rate, can the gap between them ever shrink?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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