Solve a system by adding or subtracting the equations

Answer Key - Grade 8 Math Worksheet

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

1. 1.

   Jun adds 2x + 3y = 15 and -3x - 3y = -21, since the y terms are opposites. What is the solution (x, y)?

   (6, 1)
2. 2.

   Ari subtracts the second equation from the first to solve 6x + 2y = 20 and 2x + 2y = 16. What is the solution (x, y)?

   (1, 7)
3. 3.

   Kira solves -3x + y = 2 and x + y = 10 by subtracting the second equation from the first. What is the solution (x, y)?

   (2, 8)
4. 4.

   Milo takes 3x + y = -7 away from -4x + y = 14, both sides. What is the solution (x, y)?

   (-3, 2)
5. 5.

   Noah wants y to cancel in 3x + 2y = 13 and 5x - 2y = 11. Which step makes the y terms cancel?

   • Subtract the second equation from the first.
   • Add the two equations.
   • Multiply only the first equation by 2.
6. 6.

   Tala stares at -2x + 5y = 4 and 3x - 5y = 1 for a long moment. Which step makes the y terms cancel?

   • Add the two equations.
   • Subtract the second equation from the first.
   • Multiply only the first equation by 2.
7. 7.

   Ren wants y to cancel in 2x + 3y = 12 and 5x + 3y = 21. Which step makes the y terms cancel?

   • Add the two equations.
   • Subtract the second equation from the first.
   • Multiply only the first equation by 2.
8. 8.

   Esme plans the first move for 4x - 2y = 6 and x - 2y = -3. Which step makes the y terms cancel?

   • Multiply only the first equation by 2.
   • Add the two equations.
   • Subtract the second equation from the first.
9. 9.

   Jun tries elimination on 2x + 5y = 7 and -2x - 5y = -7. How many solutions does the system have?

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

    Ari tries elimination on 2x + 3y = 8 and 2x - 3y = 8. How many solutions does the system have?

    • no solution
    • exactly one solution
    • infinitely many solutions