Solve a system by adding or subtracting the equations

Answer Key - Grade 8 Math Worksheet - Building Confidence

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

1. 1.

   Milo adds 2x + y = 11 and x - y = 1, and the y terms vanish like magic: 3x = 12. What is the solution (x, y)?

   (4, 3)
2. 2.

   Esme solves x + 2y = 13 and 3x - 2y = 7. Adding the equations gives 4x = 20. What is the solution (x, y)?

   (5, 4)
3. 3.

   A puzzle on the board says 3x + y = 17 and 2x - y = 8. Ren adds the two equations and gets 5x = 25. What is the solution (x, y)?

   (5, 2)
4. 4.

   Bo's puzzle card has 4x + 3y = 29 and 2x + 3y = 19. Subtracting the second from the first gives 2x = 10. What is the solution (x, y)?

   (5, 3)
5. 5.

   Luz takes 2x + 3y = 13 away from 6x + 3y = 21, part by part. What new equation does Luz get?

   • 8x + 6y = 34
   • 4x = 34
   • 4x + 6y = 8
   • 4x = 8
6. 6.

   Ari multiplies both sides of 2x + y = 7 by 3 to get ready for elimination. Which equation does Ari get?

   • 6x + y = 21
   • 6x + 3y = 7
   • 2x + y = 21
   • 6x + 3y = 21
7. 7.

   Ren solves 2x - y = 4 and -2x + y = 3 by adding the equations. The new equation is 0 = 7. How many solutions does the system have?

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

   Esme solves x - 2y = 3 and -x + 2y = -3 by adding the equations. The new equation is 0 = 0. How many solutions does the system have?

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

   Tala solves x + 2y = 6 and x - 2y = 6 by subtracting the second from the first. The new equation is 4y = 0. How many solutions does the system have?

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

    Zee solves 3x + y = 6 and 3x - y = 6 by subtracting the second from the first. The new equation is 2y = 0. How many solutions does the system have?

    • exactly one solution
    • no solution
    • infinitely many solutions