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

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

Grade 8 Math Worksheet - Challenge Me

NameDate

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

  1. Noah's bean plant is 5 cm and grows 4 cm a week. The pea plant grows 2 cm a week and was 17 cm after 2 weeks. Which point (weeks, cm) shows equal heights?

  2. Pia's red kite is 8 m up, climbing 5 m a minute. A green kite climbs 2 m a minute and was 29 m up after 3 minutes. Which point (minutes, m) shows them level?

  3. Ren measures snow on two hills. Sunny hill: 36 cm, melting 5 cm a day. Shady hill: melting 2 cm a day, 20 cm after 2 days. Which point (days, cm) shows equal depths?

  4. Kira watches two kites climb 3 m a minute each. The red kite starts 10 m up and the blue kite 25 m up. Will they ever be at the same height?

    • Never: they stay 15 m apart.
    • At every minute: they climb at the same speed.
    • At exactly one minute: the red kite catches up.

  5. Two kites at Zee's club start 6 m up. The red kite climbs 4 m a minute, the blue kite 2 m a minute. Are they ever at the same height?

    • Exactly once: at the start, minute 0.
    • Every minute: they start at the same height.
    • Never: one climbs faster than the other.

  6. Tala graphs the heights of a rising kite and a kite coming down. The lines cross at (5, 30). What does that point mean?

    • At the start, both kites are 30 m high.
    • After 30 minutes, both kites are 5 m high.
    • After 5 minutes, the kites are 30 m apart.
    • After 5 minutes, both kites are 30 m high.

  7. Jun graphs the heights of a bean plant and a sunflower. The lines cross at (6, 15). What does that point mean?

    • At the start, both plants are 15 cm tall.
    • After 6 weeks, both plants are 15 cm tall.
    • After 15 weeks, both plants are 6 cm tall.
    • After 6 weeks, the plants are 15 cm apart.

  8. Read this first

    Use this

    Two tables (x | y). Table A: 0 | 0; 1 | 3; 2 | 6; 3 | 9; 4 | 12. Table B: 0 | 6; 1 | 5; 2 | 4; 3 | 3; 4 | 2.

  9. Ren sees that no row is in both tables, though the lines do cross. At which point (x, y), written with decimals, do the lines cross?

  10. Pia looks at the system x + 2y = 7 and x + 2y = 10 without graphing it. How many solutions does the system have?

    • infinitely many solutions
    • exactly one solution
    • no solution

  11. Milo solves the system 3x + y = 4 and 3x + y = -2 just by looking. How many solutions does the system have?

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

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