Solve a system by substitution
Grade 8 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Kira's riddle card has two clues: y = 2x and x + y = 12. Replacing y with 2x gives x + (2x) = 12. What is the solution (x, y)?
Noah solves y = 3x and x + y = 20, pencil tapping. Putting 3x in for y gives x + (3x) = 20. What is the solution (x, y)?
Esme solves y = x + 2 and x + y = 14. Replacing y with x + 2 gives x + (x + 2) = 14. What is the solution (x, y)?
A puzzle on the board says y = 4x and 2x + y = 18. Ren replaces y with 4x and gets 2x + (4x) = 18. What is the solution (x, y)?
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Two rules (x = weeks, y = height in cm). Bean plant: y = 2x + 3. Sunflower: y = x + 7.
Pia's bean plant is racing the sunflower. Pia sets the two height rules equal: 2x + 3 = x + 7. At which point (weeks, cm) are the two plants the same height?
Use this
Two rules (x = minutes, y = height in m). Red kite: y = 3x + 2. Blue kite: y = x + 14.
Two kites rise, and one gets stuck in a slow breeze. Luz sets the rules equal: 3x + 2 = x + 14. At which point (minutes, m) are the kites level?
Milo has the system y = 2x + 1 and 4x + 2y = 26. Which equation comes next when Milo replaces y with 2x + 1?
- 4x + 2(2x + 1) = 26
- 4x + 2y = 2x + 1
- 4(2x + 1) + 2y = 26
- 4x + 4x + 1 = 26
Noah solves y = 3x + 2 and y = 3x - 4 by substitution. The work ends with the line 2 = -4. How many solutions does the system have?
- exactly one solution
- infinitely many solutions
- no solution
Pia solves y = 2x + 1 and 4x - 2y = -2 by substitution. The work ends with the line -2 = -2. How many solutions does the system have?
- infinitely many solutions
- exactly one solution
- no solution
Zee solves y = 2x + 5 and y = -x + 5 by substitution. The work ends with the line 3x = 0. How many solutions does the system have?
- no solution
- infinitely many solutions
- exactly one solution