systems of three equations: solve, and count the solutions
Grade 11 Math Worksheet - Building Confidence
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 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
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
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)
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
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)
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?