Solve a system by substitution
Grade 8 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
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)?
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
- 2x + 3y = x - 3
- 2(x - 3) + 3y = 21
Milo has the system y = 2x + 1 and 4x + 2y = 26. Which equation comes next when Milo replaces y with 2x + 1?
- 4x + 2y = 2x + 1
- 4(2x + 1) + 2y = 26
- 4x + 2(2x + 1) = 26
- 4x + 4x + 1 = 26
A homework card shows y = x + 4 and 3x + 5y = 44. Which equation comes next when Zee replaces y with x + 4?
- 3x + 5(x + 4) = 44
- 3x + 5y = x + 4
- 3(x + 4) + 5y = 44
- 3x + 5x + 4 = 44
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 first equation.
- No: it works only in the second equation.
- Yes: it works in both equations.
- No: it works in neither equation.
Bo guesses that (3, 5) solves y = 3x and x + 2y = 13, a lucky guess maybe. Is (3, 5) a solution of the system?
- Yes: it works in both equations.
- No: it works in neither equation.
- No: it works only in the second equation.
- 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?
- no solution
- exactly one solution
- infinitely many solutions
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?
- exactly one solution
- infinitely many solutions
- no solution