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

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

2. 1.

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

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

   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
4. 3.

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

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

   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
6. 5.

   An adult volunteer at the school fair snack table records three orders in the table. Esme works out the prices. Which prices fit all three orders?

   • cookie $0.50, apple $1, milk carton $0.75
   • cookie $1, apple $0.50, milk carton $0.75
   • cookie $1.25, apple $0.25, milk carton $0.75
   • cookie $1, apple $0.50
7. 6.

   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, white jar $2.50
   • red jar $5.75, blue jar $3, white jar $0.50
   • red jar $3.50, blue jar $4, white jar $2.50
   • red jar $4, blue jar $3.50
8. 7.

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

   • yellow jar $3, green jar $4.50, black jar $2
   • yellow jar $4.50, green jar $3, black jar $2
   • yellow jar $2.75, green jar $4.25, black jar $3.50
   • yellow jar $3, green jar $4.50
9. 8.

   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
10. 9.

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

    -5
11. 10.

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

    13