Grade 9 · Math · Algebra 1

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

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

Grade 9 Math Worksheet

NameDate

Circle the best answer.

1.
Esme compares y = -3x + 8 and 3x + y = 5. How many solutions does the system have?
- Infinitely many solutions (dependent)
- No solution (inconsistent)
- One solution (independent)
2.
Jun checks y = 3x - 2 and 3x + y = 7. How many solutions does the system have?
- Infinitely many solutions (dependent)
- No solution (inconsistent)
- One solution (independent)
3.
Kira reads y = 2x + 5 and y - 2x = 5. How many solutions does the system have?
- No solution (inconsistent)
- One solution (independent)
- Infinitely many solutions (dependent)
4.
Luz sorts y = 6 - x and x + y = 6. How many solutions does the system have?
- Infinitely many solutions (dependent)
- No solution (inconsistent)
- One solution (independent)
5.
Milo compares y = -x + 4 and x + y = 9. How many solutions does the system have?
- One solution (independent)
- No solution (inconsistent)
- Infinitely many solutions (dependent)
6.
Tala studies 2x - y = 4 and 6x - 3y = 12. How many solutions does the system have?
- Infinitely many solutions (dependent)
- No solution (inconsistent)
- One solution (independent)
7.
Zee compares 3x + 2y = 3 and 6x + 4y = 9. How many solutions does the system have?
- No solution (inconsistent)
- Infinitely many solutions (dependent)
- One solution (independent)
8.
Ari looks at x + 4y = 8 and 2x + 8y = 16. How many solutions does the system have?
- One solution (independent)
- Infinitely many solutions (dependent)
- No solution (inconsistent)
9.
Luz starts on 2x + 3y = 13 and 3x + 2y = 12. Which single first step leaves an equation with only one letter?
- Multiply the first equation by 3 and the second by 2, then subtract
- Subtract the second equation from the first
- Add the two equations
- Multiply the first equation by 2, then subtract the second
10.
Milo starts on 5x + 2y = 19 and 3x - 4y = 1. Which single first step leaves an equation with only one letter?
- Multiply the second equation by 2, then add the first
- Multiply the first equation by 2, then add the second
- Add the two equations
- Subtract the second equation from the first

9th grade Systems: one, none or infinitely many solutions, and the quickest method worksheet – printable — Print: 1 2 3 4 5 6

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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