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

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Esme compares y = -3x + 8 and 3x + y = 5. How many solutions does the system have?

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

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

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

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

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

   Tala studies 2x - y = 4 and 6x - 3y = 12. How many solutions does the system have?

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

   Ari looks at x + 4y = 8 and 2x + 8y = 16. How many solutions does the system have?

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

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

   • One solution (independent)
   • Infinitely many solutions (dependent)
   • No solution (inconsistent)
7. 7.

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

   • Subtract the second equation from the first
   • Replace y in the second equation with 2x + 1
   • Add the two equations
   • Multiply the first equation by 3, then subtract the second
8. 8.

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

   Luz starts on 2x + 3y = 13 and 3x + 2y = 12. Which single first step leaves an equation with only one letter?

   • Subtract the second equation from the first
   • Multiply the first equation by 2, then subtract the second
   • Multiply the first equation by 3 and the second by 2, then subtract
   • 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?

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