Grade 11 · Math · Algebra 2

11th grade Systems of three equations: solve, and count the solutions worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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systems of three equations: solve, and count the solutions

Grade 11 Math Worksheet - Building Confidence

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

Read this first
Use the table
Equations: (1) 2x − 3y − z = -4; (2) 4x − 4y − z = -11; (3) -3x − 2y − 2z = 16.
x y z total
(1) 2 -3 -1 -4
(2) 4 -4 -1 -11
(3) -3 -2 -2 16
1.
Bo sees that rows (1) and (2) both have -z, so subtracting row (2) from row (1) cancels z. Which new row is left?
- -2x − 7y = -15
- -2x + y = -15
- 6x − 7y − 2z = -15
- -2x + y = 7
2.
In Esme's number table, rows (1) and (2) share 2z. Esme takes row (2) away from row (1). Which new row is left?
- -6x − 7y = 6
- -6x + y = 6
- -6x + y = 10
- 2x − 7y + 4z = 6
3.
Kira cancelled z using rows (1) and (2) of the number table. Which step on rows (1) and (3) also cancels z?
- Add rows (1) and (3)
- Subtract row (3) from row (1)
- Subtract row (3) from 2 × row (1)
4.
Rows (1) and (2) of Luz's table have already cancelled z. Which step on rows (1) and (3) cancels z as well?
- Subtract row (3) from row (1)
- Add 2 × row (1) to row (3)
- Add rows (1) and (3) straight across
5.
Milo has a new row without z from rows (1) and (2). Which step on rows (1) and (3) also cancels z?
- Add rows (1) and (3)
- Subtract row (3) from 2 × row (1)
- Add 2 × row (1) to row (3)
6.
Noah wants a second row without z, made from rows (1) and (3). Which step does that?
- Add 2 × row (1) to row (3)
- Subtract row (3) from row (1)
- Add rows (1) and (3)
Pia found x = -1 and y = -1. Row (1) of the number table says -2x + 3y + z = -6. What is z?
Working on the number table, Ren has x = -4 and y = 5. Row (1) is 4x − 4y + z = -30. What is z?
Tala solved the two-letter rows: x = 6 and y = 6. Row (1) reads x − 3y + z = -5. What is z?
Ari knows x = 5 and y = 5, and row (1) of the table is -3x − 2y + z = -19. What is z?

	x	y	z	total
(1)	2	-3	-1	-4
(2)	4	-4	-1	-11
(3)	-3	-2	-2	16

11th grade Systems of three equations: solve, and count the solutions worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Systems of three equations: solve, and count the solutions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can write a system as a number table and cancel a letter by adding or subtracting rows.
I can cancel the same letter from two pairs of rows, solve, and give the answer as (x, y, z).
I can tell from the rows whether a system has one solution, none or infinitely many.

Words to know

system of three equations: Three equations that share the letters x, y and z.

number table: The system's numbers: one row per equation, one column per letter, then the total.

eliminate: Add or subtract rows so one letter's numbers cancel to 0.

ordered triple: An answer (x, y, z), written in that order.

no solution: No triple fits all three rows; a row says 0 = 5.

infinitely many solutions: A row is built from the others, so 0 = 0.

Common mistakes

Took away a negative number as if it were positive.

Subtracted the letter columns but added the totals. Ask your child to subtract every column of the table, the total too.

Cancelled one letter from the first pair of equations and a different letter from the second.

What to say

Ask: what is 5 − (−2)? Taking away a negative adds.

Ask: which letter did you cancel first? Cancel that one again.

Questions parents ask

What is the most common mistake with systems of three equations: solve, and count the solutions?

Took away a negative number as if it were positive.

How can I help my child with systems of three equations: solve, and count the solutions?

Ask: what is 5 − (−2)? Taking away a negative adds.

Are these 11th 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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