Solve a system by adding or subtracting the equations

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Zee multiplies 2x + y = 7 by 2, then adds it to 3x - 2y = 7. What is the solution (x, y)?

   (3, 1)
2. 2.

   To solve x + y = 11 and -x - 2y = -15, Noah first multiplies x + y = 11 by 2, then adds. What is the solution (x, y)?

   (7, 4)
3. 3.

   Ren multiplies x + y = 2 by 3 so the y terms become opposites in x - 3y = -14. What is the solution (x, y)?

   (-2, 4)
4. 4.

   Milo tries elimination on x - 3y = 2 and 3x - 9y = 6, multiplying one equation first. How many solutions does the system have?

   • infinitely many solutions
   • no solution
   • exactly one solution
5. 5.

   Pia finds 2x + y = 5 and 6x + 3y = 15 in a puzzle book with a page missing. How many solutions does the system have?

   • infinitely many solutions
   • no solution
   • exactly one solution
6. 6.

   Jun tries elimination on 2x + y = 4 and 3x + 2y = 8, multiplying one equation first. How many solutions does the system have?

   • no solution
   • exactly one solution
   • infinitely many solutions
7. 7.

   Luz finds x + 3y = 6 and 2x + 5y = 12 in a puzzle book with a page missing. How many solutions does the system have?

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

   Kira measures two sunflowers, x cm and y cm tall: x + y = 250 and x - y = 30. What point (taller cm, shorter cm) solves the system?

   (140, 110)
9. 9.

   Snow piles up in two drifts, x cm and y cm deep: x + y = 90 and x - y = 24. Ari solves it. What point (deep cm, small cm) solves the system?

   (57, 33)
10. 10.

    Milo reads a mystery book (x pages) and a comic (y pages): x + y = 300 and x - y = 120. What point (mystery, comic) solves the system?

    (210, 90)