Systems: one, none or infinitely many solutions, and the quickest method

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Kira reads y = 2x + 5 and y - 2x = 5. How many solutions does the system have?

   • Infinitely many solutions (dependent)
   • One solution (independent)
   • No solution (inconsistent)
2. 2.

   Noah tests y = 2x + 1 and 2x + y = 9. How many solutions does the system have?

   • Infinitely many solutions (dependent)
   • One solution (independent)
   • No solution (inconsistent)
3. 3.

   Pia reads 2x + 3y = 12 and 4x + 6y = 18. How many solutions does the system have?

   • No solution (inconsistent)
   • One solution (independent)
   • Infinitely many solutions (dependent)
4. 4.

   Ren checks 3x + 2y = 8 and 3x - 2y = 8. How many solutions does the system have?

   • Infinitely many solutions (dependent)
   • No solution (inconsistent)
   • One solution (independent)
5. 5.

   Bo sorts 4x - 2y = 6 and 4x + 2y = 6. How many solutions does the system have?

   • No solution (inconsistent)
   • One solution (independent)
   • Infinitely many solutions (dependent)
6. 6.

   Esme starts on y = 2x + 1 and 3x + 2y = 16. Which single first step leaves an equation with only one letter?

   • Add the two equations
   • Multiply the first equation by 3, then subtract the second
   • Replace y in the second equation with 2x + 1
   • Subtract the second equation from the first
7. 7.

   Jun starts on 3x + 2y = 16 and 5x - 2y = 8. Which single first step leaves an equation with only one letter?

   • Multiply the second equation by 3, then add the first
   • Multiply the first equation by 2, then subtract the second
   • Add the two equations
   • Subtract the second equation from the first
8. 8.

   Kira starts on 4x + 3y = 17 and 4x + y = 11. Which single first step leaves an equation with only one letter?

   • Multiply the first equation by 3, then subtract the second
   • Subtract the second equation from the first
   • Multiply the second equation by 2, then add the first
   • Add the two equations
9. 9.

   Milo starts on 5x + 2y = 19 and 3x - 4y = 1. Which single first step leaves an equation with only one letter?

   • Subtract the second equation from the first
   • Multiply the second equation by 2, then add the first
   • Multiply the first equation by 2, then add the second
   • Add the two equations
10. 10.

    Noah starts on x = 3y - 2 and 2x + 5y = 18. Which single first step leaves an equation with only one letter?

    • Subtract the second equation from the first
    • Replace x in the second equation with 3y - 2
    • Multiply the second equation by 3, then subtract the first
    • Add the two equations