systems of three equations: solve, and count the solutions

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. Read this first

   Use the table

   Equations: (1) -4x + 4y + z = 8; (2) 5x − y + z = -13; (3) -3x + 2y + 3z = 18.

   	x	y	z	total
   (1)	-4	4	1	8
   (2)	5	-1	1	-13
   (3)	-3	2	3	18

2. 1.

   Rows (1) and (2) of Ari's number table both have z. Ari subtracts row (2) from row (1). Which new row is left?

   • x + 3y + 2z = -5
   • -9x + 5y = 21
   • -9x + 5y = -5
   • -9x + 3y = -5
3. 2.

   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
   • -2x + y = 7
   • 6x − 7y − 2z = -15
4. 3.

   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 + y = 10
   • 2x − 7y + 4z = 6
   • -6x + y = 6
   • -6x − 7y = 6
5. 4.

   Jun cancels z by subtracting row (2) from row (1), since both rows have -2z. Which new row is left?

   • -5x − 3y = -6
   • x + y = 14
   • -5x − 3y − 4z = 14
   • x + y = -6
6. 5.

   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
7. 6.

   Milo has a new row without z from rows (1) and (2). Which step on rows (1) and (3) also cancels z?

   • Add 2 × row (1) to row (3)
   • Subtract row (3) from 2 × row (1)
   • Add rows (1) and (3)
8. 7.

   Noah wants a second row without z, made from rows (1) and (3). Which step does that?

   • Add rows (1) and (3)
   • Add 2 × row (1) to row (3)
   • Subtract row (3) from row (1)
9. 8.

   Working on the number table, Ren has x = -4 and y = 5. Row (1) is 4x − 4y + z = -30. What is z?

   6
10. 9.

    Tala solved the two-letter rows: x = 6 and y = 6. Row (1) reads x − 3y + z = -5. What is z?

    7
11. 10.

    Ari knows x = 5 and y = 5, and row (1) of the table is -3x − 2y + z = -19. What is z?

    6