Question

Create 3 equations that could go into a system with the given equation that will result in one solution, no solution, and infinitely many solutions. Then solve them to ensure they work.

a) x + 2y = 8; 2x + 4y = 12; 3x + 6y = 16 (One solution)
b) 3x - y = 5; 6x - 2y = 10; 9x - 3y = 15 (No solution)
c) 2x + 3y = 10; 4x + 6y = 20; 6x + 9y = 30 (Infinitely many solutions)
d) x - y = 3; 2x - 2y = 6; 3x - 3y = 9 (No solution)

Answer 1

To create a system with one solution, use three independent equations. To create a system with no solution, use inconsistent equations. To create a system with infinitely many solutions, use dependent equations.

Step-by-step explanation:

To create a system of equations with one solution, you need three independent equations. For example:

Equation 1: x + 2y = 8

Equation 2: 2x + 4y = 12

Equation 3: 3x + 6y = 16

To create a system of equations with no solution, you need inconsistent equations. For example:

Equation 1: 3x - y = 5

Equation 2: 6x - 2y = 10

Equation 3: 9x - 3y = 15

To create a system of equations with infinitely many solutions, you need dependent equations. For example:

Equation 1: 2x + 3y = 10

Equation 2: 4x + 6y = 20

Equation 3: 6x + 9y = 30