Systems: one, none or infinitely many solutions, and the quickest method
Grade 9 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
Pia writes 2x + 3y = 12 and 4x + ky = 20. For which k does the system have no solution?
Ren writes 3x + 4y = 10 and 6x + ky = 15. For which k does the system have no solution?
Tala writes 2x + 5y = 7 and 6x + 15y = c. For which c does the system have infinitely many solutions?
Zee writes 4x + 6y = 10 and 6x + ky = 15. For which k does the system have infinitely many solutions?
Bo compares y = 3(x - 2) and y = 3x - 6. How many solutions does the system have?
- One solution (independent)
- No solution (inconsistent), since the two rules look different
- Infinitely many solutions (dependent)
Esme checks y = 2(x + 3) and y = 2x + 3. How many solutions does the system have?
- Infinitely many solutions (dependent)
- One solution (independent)
- No solution (inconsistent)
Kira reads 2(x + y) = 10 and x + y = 5. How many solutions does the system have?
- No solution (inconsistent)
- Infinitely many solutions (dependent)
- One solution (independent)
Read this first
Old system
x + 2y = 10 and x - y = 1. New system: -x + 4y = 8 and x - y = 1.
Milo replaces the first equation with "first - 2 × second". The old solution is (4, 3). Which point solves the new system?
- (8, 6)
- (0, 2)
- (3, 4)
- (4, 3)
Old system
3x + 2y = 16 and 2x - y = 6. New system: 7x = 28 and 2x - y = 6.
Noah replaces the first equation with "first + 2 × second". The old solution is (4, 2). Which point solves the new system?
- (8, 4)
- (2, 4)
- (4, 2)
- (4, 0)
Old system
x + 3y = 7 and 2x - y = 7. New system: -3x + 5y = -7 and 2x - y = 7.
Pia replaces the first equation with "first - 2 × second". The old solution is (4, 1). Which point solves the new system?
- (4, 1)
- (8, 2)
- (1, 4)
- (-1, -2)