systems of three equations: solve, and count the solutions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. Read this first

   Use the table

   Equations: (1) 3x − y + z = -2; (2) 4x − 4y + 4z = 5; (3) 2x + 2y − 2z = -9.

   	x	y	z	total
   (1)	3	-1	1	-2
   (2)	4	-4	4	5
   (3)	2	2	-2	-9

2. 1.

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

   • No solution
   • Exactly one solution
   • Infinitely many solutions
3. 2.

   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
4. 3.

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

   • Exactly one solution
   • No solution
   • Infinitely many solutions
5. 4.

   Bo'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
6. 5.

   An adult at the school play snack stand writes three orders in the table. Kira finds each price. Which prices fit all three orders?

   • muffin $0.75, banana $0.50, juice $2.25
   • muffin $1.25, banana $0.25, juice $1
   • muffin $1.25, banana $0.25
   • muffin $0.25, banana $1.25, juice $1
7. 6.

   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
8. 7.

   Row (3) of Milo's number table has its total missing, shown as c. For which c does the system have infinitely many solutions?

   -22
9. 8.

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

   -5
10. 9.

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

    13
11. 10.

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

    -13