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.

   Pia solves 3x + 4y = -7 and x - 4y = 19 by adding the equations. What is the solution (x, y)?

   (3, -4)
2. 2.

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

   (6, 1)
3. 3.

   Luz's warm-up card says 4x + 2y = -4 and 5x - 2y = -23 (the card also has a smiley face). What is the solution (x, y), found by adding?

   (-3, 4)
4. 4.

   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)
5. 5.

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

   (-3, 2)
6. 6.

   Noah wants y to cancel in 3x + 2y = 13 and 5x - 2y = 11. 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.
7. 7.

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

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

   Bo tries elimination on 4x - y = 3 and -4x + y = 5. How many solutions does the system have?

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

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

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

    Kira gets 4x + 5y = -12 and -4x + 5y = 12 as a bonus question (the prize is a high five). How many solutions does the system have?

    • exactly one solution
    • no solution
    • infinitely many solutions