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.

   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)?

   (5, 15)
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 = weeks, y = height in cm). Bean plant: y = 2x + 3. Sunflower: y = x + 7.

5. 4.

   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?

   (4, 11)

6. Use this

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

7. 5.

   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)
8. 6.

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

   • 3x + 5y = x + 4
   • 3(x + 4) + 5y = 44
   • 3x + 5(x + 4) = 44
   • 3x + 5x + 4 = 44
9. 7.

   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 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.
10. 8.

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

    • No: it works only in the second equation.
    • Yes: it works in both equations.
    • No: it works in neither equation.
    • No: it works only in the first equation.
11. 9.

    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
12. 10.

    Ren checks a system on scrap paper: y = 4x - 1 and y = 2x - 1. Substitution ends with 2x = 0. How many solutions does the system have?

    • exactly one solution
    • no solution
    • infinitely many solutions