Solve a system by substitution

Answer Key - Grade 8 Math Worksheet

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

1. 1.

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

   (-3, 7)
2. 2.

   Ari finds y = 2x + 5 and -3x + 4y = 10 on a puzzle card (the card is a little crumpled). What is the solution (x, y)?

   (-2, 1)
3. 3.

   Bo solves y = -x + 3 and 5x + 3y = 17 by putting the rule for y into the other equation. What is the solution (x, y)?

   (4, -1)
4. 4.

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

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

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

   Ari looks at the system y = 3x - 2 and 6x - 2y = 4 and tries substitution. How many solutions does the system have?

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

   Tala gets y = -2x + 3 and 4x + 2y = 6 as a bonus question (the bonus is bragging rights). How many solutions does the system have?

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

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

    • infinitely many solutions
    • exactly one solution
    • no solution