Grade 8 · Math

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

NameDate

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

Esme graphs two lines for a puzzle page and draws a tiny star where they meet. At which point (x, y) do line A and line B cross?
Zee sketches two lines that cross left of the y-axis. At which point (x, y) do line A and line B cross?
Read this first
Use this
Two tables (hours | °F), only three rows each. Town A: 0 | -8; 1 | -4; 2 | 0. Town B: 0 | 4; 1 | 5; 2 | 6.
On a cold morning, Luz records the temperature in two towns every hour. Both keep warming at a steady rate. At which point (hours, °F) are the towns equally warm?
Pia wants the point that works in both y = -2x + 5 and y = x + 8, with no guessing. At which point (x, y) do the two lines cross?
5.
Milo tests the point (3, -1) on the system y = -x + 2 and y = 2x - 7. Is (3, -1) a solution of the system?
- Yes: it works in both equations.
- No: it works only in the second equation.
- No: it works in neither equation.
- No: it works only in the first equation.
6.
Ari checks the point (2, -4) for the system y = x - 5 and y = -3x + 2 twice, just to be sure. Is (2, -4) a solution of the system?
- No: it works in neither equation.
- No: it works only in the first equation.
- No: it works only in the second equation.
- Yes: it works in both equations.
7.
Kira copies the system y = 2x + 5 and y = 5 + 2x from the board. How many solutions does the system have?
- infinitely many solutions
- exactly one solution
- no solution
Bo's bean plant is 6 cm tall and grows 3 cm a week. The sunflower is 14 cm tall and grows 1 cm a week. At which point (weeks, cm) are they the same height?
A red kite is 12 m up and climbs 3 m a minute. Ari's blue kite is 30 m up and climbs 1 m a minute. At which point (minutes, m) are they level?
Tala has read 50 pages of a mystery and 20 pages of a comic. Each day, Tala reads 10 more mystery pages and 16 comic pages. At which point (days, pages) do the totals match?

8th grade Solve a system by graphing: one, none or infinitely many solutions worksheet – printable — Print: 1 2 3 4 5 6

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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