21.11.1. Definition

Try these first

1. 1.

   Define a system of linear equations.

   Hint

   Think about the number of equations and variables.

2. 2.

   What does consistent mean in the context of a system?

   Hint

   Consider what happens if you can find a solution.

3. 3.

   What defines a system of linear equations?

   • A single linear equation
   • Multiple linear equations with the same variables
   • Only equations involving two variables

   Hint

   Think about what a 'system' implies in mathematics.

4. 4.

   True or False: An inconsistent system has at least one solution.

   • True
   • False

   Hint

   Reflect on the meaning of inconsistent.

5. 5.

   Given the system of equations: 5x - 3y = 12 and 15x - 9y = 36, determine the nature of the system and support your justification.

   Hint

   Check if one equation is a scalar multiple of the other.

6. 6.

   Use Gauss elimination to solve the following equations: 2x + y = 8, 4x - 3y = -2.

   Hint

   Focus on getting zeros below the leading coefficients.