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.

   Kira's riddle card says x + y = 10 and x - y = 4. Adding the two equations gives 2x = 14. What is the solution (x, y)?

   (7, 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.

   Noah solves 3x + 2y = 16 and x + 2y = 8. Subtracting the second equation from the first gives 2x = 8. What is the solution (x, y)?

   (4, 2)
4. 4.

   Tala takes x + y = 10 away from 4x + y = 22, and y disappears: 3x = 12. What is the solution (x, y)?

   (4, 6)
5. 5.

   Zee adds x + 3y = 11 and 2x - 3y = 4 to clear y. What new equation does Zee get?

   • -x + 6y = 7
   • 3x + 6y = 15
   • 3x = 15
   • 3x = 7
6. 6.

   Pia lines up 2x + 5y = 19 and 4x - 5y = 11, then adds the two equations, very neatly. What new equation does Pia get?

   • 6x + 10y = 30
   • 6x = 8
   • -2x + 10y = 8
   • 6x = 30
7. 7.

   Jun subtracts 2x + 4y = 14 from 5x + 4y = 23 to clear y. What new equation does Jun get?

   • 3x = 37
   • 3x = 9
   • 7x + 8y = 37
   • 3x + 8y = 9
8. 8.

   Kira doubles every part of x - 2y = 4, like doubling a recipe. Which equation does Kira get?

   • 2x - 4y = 8
   • 2x - 2y = 8
   • 2x - 4y = 4
   • x - 2y = 8
9. 9.

   Milo multiplies both sides of 3x + 2y = 5 by 4. Which equation does Milo get?

   • 12x + 2y = 20
   • 3x + 2y = 20
   • 12x + 8y = 20
   • 12x + 8y = 5
10. 10.

    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