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)?
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?
Tala solves y = x - 3 and 2x + 3y = 21 by substitution, eraser ready. Which equation comes next when Tala replaces y with x - 3?
- 2x + 3x - 3 = 21
- 2x + 3(x - 3) = 21
- 2(x - 3) + 3y = 21
- 2x + 3y = x - 3
Ari thinks (3, 5) might solve the system y = 2x - 1 and x + y = 9. Is (3, 5) a solution of the system?
- No: it works only in the second equation.
- No: it works in neither equation.
- Yes: it works in both equations.
- No: it works only in the first equation.
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
Luz checks a system on scrap paper: y = x + 5 and x - y = 1. Substitution ends with -5 = 1. How many solutions does the system have?
- infinitely many solutions
- exactly one solution
- no solution
Milo checks a system on scrap paper: y = x - 3 and 3x - 3y = 9. Substitution ends with 9 = 9. How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one 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?
- exactly one solution
- infinitely many solutions
- no solution