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.

   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)
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. Read this first

   Use this

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

4. 3.

   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)

5. Use this

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

6. 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)

7. Use this

   Two rules (x = minutes, y = height in m). Red kite: y = 3x + 2. Blue kite: y = x + 14.

8. 5.

   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?

   (6, 20)
9. 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 only in the second equation.
   • No: it works in neither equation.
   • No: it works only in the first equation.
   • Yes: it works in both equations.
10. 7.

    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?

    • infinitely many solutions
    • no solution
    • exactly one solution
11. 8.

    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
12. 9.

    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?

    • no solution
    • infinitely many solutions
    • exactly one solution
13. 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?

    • no solution
    • infinitely many solutions
    • exactly one solution