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.

   Jun has the system y = 4x + 6 and y = 2x - 2. What is the solution (x, y), found by substitution?

   (-4, -10)
3. 3.

   Kira solves the system y = x - 2 and 5x - 3y = 18 by substitution. What is the solution (x, y)?

   (6, 4)
4. 4.

   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)
5. 5.

   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)
6. 6.

   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 only in the first equation.
   • No: it works only in the second equation.
   • 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?

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

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

   • exactly one solution
   • no solution
   • infinitely many solutions
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