Solve a system by substitution

Answer Key - Grade 8 Math Worksheet - Building Confidence

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

1. 1.

   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)?

   (4, 8)
2. 2.

   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)?

   (6, 8)
3. 3.

   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)?

   (3, 12)

4. Read this first

   Use this

   Two rules (x = days, y = snow depth in cm). Sunny yard: y = -5x + 40. Shady yard: y = -2x + 25.

5. 4.

   Snow melts in two yards. Jun sets the two depth rules equal: -5x + 40 = -2x + 25. At which point (days, cm) is the snow the same depth in both yards?

   (5, 15)
6. 5.

   A homework card shows y = x + 4 and 3x + 5y = 44. Which equation comes next when Zee replaces y with x + 4?

   • 3x + 5x + 4 = 44
   • 3x + 5(x + 4) = 44
   • 3x + 5y = x + 4
   • 3(x + 4) + 5y = 44
7. 6.

   Bo guesses that (3, 5) solves y = 3x and x + 2y = 13, a lucky guess maybe. Is (3, 5) a solution of the system?

   • No: it works in neither equation.
   • No: it works only in the first equation.
   • Yes: it works in both equations.
   • No: it works only in the second equation.
8. 7.

   Kira gets (3, 7) for the system y = 2x + 1 and 3x + y = 16. Is (3, 7) a solution of the system?

   • Yes: it works in both equations.
   • No: it works only in the second equation.
   • No: it works only in the first equation.
   • No: it works in neither equation.
9. 8.

   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
   • infinitely many solutions
   • exactly one solution
10. 9.

    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?

    • exactly one solution
    • no solution
    • infinitely many solutions
11. 10.

    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?

    • infinitely many solutions
    • exactly one solution
    • no solution