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8th grade Solve a system by graphing: one, none or infinitely many solutions worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Solve a system by graphing: one, none or infinitely many solutions

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

  1. Read this first

    Use this

    Two tables (weeks | cm). Bean plant: 0 | 4; 1 | 7; 2 | 10; 3 | 13; 4 | 16. Sunflower: 0 | 10; 1 | 11; 2 | 12; 3 | 13; 4 | 14.

  2. Kira measures a bean plant and a sunflower every week (the sunflower is in no hurry). The tables show their heights. Which point (weeks, cm) is in both tables?

  3. Use this

    Two tables (days | cm). Sunny hill: 0 | 20; 1 | 16; 2 | 12; 3 | 8; 4 | 4. Shady hill: 0 | 14; 1 | 12; 2 | 10; 3 | 8; 4 | 6.

  4. Tala checks the snow on two hills each day as it melts. The tables show the snow depth on each hill. Which point (days, cm) is in both tables?

  5. Use this

    Two tables (days | buttons). Red jar: 0 | 2; 1 | 7; 2 | 12; 3 | 17; 4 | 22. Blue jar: 0 | 10; 1 | 11; 2 | 12; 3 | 13; 4 | 14.

  6. Esme adds buttons to two craft jars every day, one button at a time. The tables show how many buttons each jar holds. Which point (days, buttons) is in both tables?

  7. Noah sketches two lines on a grid with a freshly sharpened pencil. At which point (x, y) do line A and line B cross?

  8. Ren graphs two lines for a math club challenge. At which point (x, y) do line A and line B cross?

  9. Pia tests the point (2, 5) on the system y = 2x + 1 and y = x + 3. Is (2, 5) a solution of the system?

    • No: it works only in the first equation.
    • No: it works in neither equation.
    • Yes: it works in both equations.
    • No: it works only in the second equation.

  10. Luz thinks (2, 5) might solve the system y = 3x - 1 and y = x + 4. Is (2, 5) a solution of the system?

    • No: it works in neither equation.
    • No: it works only in the first equation.
    • Yes: it works in both equations.
    • No: it works only in the second equation.

  11. Kira graphs two equations and only one line shows up on the grid. How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution

  12. Use this

    Two tables (x | y). Table A: 0 | 4; 1 | 7; 2 | 10; 3 | 13; 4 | 16. Table B: 2 | 10; 3 | 13; 4 | 16; 5 | 19; 6 | 22.

  13. Jun makes a table for each equation in a system, starting table B at a later row. Both follow steady rules. How many solutions does the system have?

    • infinitely many solutions
    • no solution
    • exactly one solution

  14. Use this

    Two tables (x | y). Table A: 0 | 2; 1 | 3; 2 | 4; 3 | 5; 4 | 6. Table B: 0 | 2; 1 | 5; 2 | 8; 3 | 11; 4 | 14.

  15. Pia makes a table for each equation in a system (neat handwriting, too). Both tables follow steady rules. How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution
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8th grade Solve a system by graphing: one, none or infinitely many solutions worksheet – printable
Print: 123456

About this worksheet

Solve a system by graphing: one, none or infinitely many solutions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the point where two lines cross, from two tables, a graph, two equations or a story, and write it as (x, y).
  • I can check whether a point solves a system by putting it into both equations.
  • I can tell whether a system has one solution, no solution (parallel lines) or infinitely many (the same line), and say what the crossing point means in a story.

Standard: 8.EE.C.8a, 8.EE.C.8b (graphing, no or infinite solutions)

Words to know

system of equations: Two equations about the same x and y, worked on together.

solution of a system: An (x, y) that makes both equations true: a row in both tables.

shared row: A row with the same x and the same y in both tables.

gap: How far apart the two outputs are in one row.

parallel lines: Lines that are equally steep and never meet.

slope / start: How much y changes for 1 more x / the y when x is 0.

Common mistakes

Your child found where the two lines meet but wrote the point backward, with the up number first.

Your child found where the two lines meet but gave only the first number, not the whole point.

Your child gave the point where one line meets the up-and-down axis, not the point where the two lines meet. Try tracing both lines with two fingers until they touch.

What to say

Ask: which number goes across, and which goes up?

Ask: at that spot, how high are the lines?

Questions parents ask

What is the most common mistake with solve a system by graphing: one, none or infinitely many solutions?

Your child found where the two lines meet but wrote the point backward, with the up number first.

How can I help my child with solve a system by graphing: one, none or infinitely many solutions?

Ask: which number goes across, and which goes up?

Are these 8th 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.

More grade 8 math

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