Solve a system by substitution

Answer Key - Grade 8 Math Worksheet

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

1. 1.

   Esme sees two rules, y = 3x - 5 and y = -x + 7, on a puzzle sheet. Both give y. What is the solution (x, y)?

   (3, 4)
2. 2.

   Tala solves y = -2x + 1 and y = x + 10 by substitution (two y's, one answer). What is the solution (x, y)?

   (-3, 7)
3. 3.

   Noah gets the system y = -2x + 4 and 2x + 2y = 14 as a warm-up. What is the solution (x, y)?

   (-3, 10)
4. 4.

   Milo thinks (2, -1) solves the system y = -2x + 3 and 3x + 2y = 6. Is (2, -1) 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.
5. 5.

   Zee tests (-2, -6) in the system y = 3x + 2 and x - 2y = 10, one equation at a time. Is (-2, -6) a solution of the system?

   • Yes: it works in both equations.
   • No: it works only in the first equation.
   • No: it works only in the second equation.
   • No: it works in neither equation.
6. 6.

   Luz gets (4, -3) for the system y = -x + 1 and 2x - 3y = 17. Is (4, -3) a solution of the system?

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

   Ren looks at the system y = 2x - 1 and 6x - 3y = 9 and tries substitution. How many solutions does the system have?

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

   Esme gets y = -x + 4 and 2x + 2y = 5 as a bonus question (the bonus is bragging rights). How many solutions does the system have?

   • no solution
   • exactly one solution
   • infinitely many solutions
9. 9.

   Bo looks at the system y = 2x + 3 and x + y = 3 and tries substitution. How many solutions does the system have?

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

    Jun gets y = -3x - 2 and 2x - y = 2 as a bonus question (the bonus is bragging rights). How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution