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Grade 11 · Math · Algebra 2

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

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systems of three equations: solve, and count the solutions

Grade 11 Math Worksheet - Challenge Me

NameDate

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

  1. Read this first

    Use the table

    Equations: (1) x − y − 2z = 4; (2) 2x − y − 2z = 2; (3) 3x − 2y − 4z = 3.

    xyztotal
    (1)1-1-24
    (2)2-1-22
    (3)3-2-43

  2. Noah writes a system of three equations as the number table shown. How many solutions does it have?

    • Infinitely many solutions
    • No solution
    • Exactly one solution

  3. Pia's math club card shows this system as a number table. How many solutions does the system have?

    • Exactly one solution
    • No solution
    • Infinitely many solutions

  4. Ren checks the system in the number table before solving it. How many solutions does it have?

    • No solution
    • Exactly one solution
    • Infinitely many solutions

  5. Tala writes a system of three equations as the number table shown. How many solutions does it have?

    • Infinitely many solutions
    • No solution
    • Exactly one solution

  6. Bo's math club card shows this system as a number table. How many solutions does the system have?

    • Infinitely many solutions
    • Exactly one solution
    • No solution

  7. The art teacher orders paint three times, shown in the table. Jun works out the price of each jar. Which prices fit all three orders?

    • red jar $4, blue jar $3.50
    • red jar $4, blue jar $3.50, white jar $2.50
    • red jar $3.50, blue jar $4, white jar $2.50
    • red jar $5.75, blue jar $3, white jar $0.50

  8. Luz's art club helper, an adult, records three paint orders in the table. Which jar prices fit all three orders?

    • yellow jar $4.50, green jar $3, black jar $2
    • yellow jar $3, green jar $4.50, black jar $2
    • yellow jar $3, green jar $4.50
    • yellow jar $2.75, green jar $4.25, black jar $3.50

  9. Noah covers the total of row (3) with the letter c. Which value of c gives the system infinitely many solutions?

  10. In Pia's table, the total of row (3) is c. For which c does the system have infinitely many solutions?

  11. Ren wants the system in the table to have infinitely many solutions. What must the missing total c be?

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