21.1. Systems of Linear Equations

Try these first

1. 1.

   Define what a system of linear equations is.

   Hint

   Involves what 'terms' they share.

2. 2.

   Provide an example of a consistent system.

   Hint

   Look for equations that intersect.

3. 3.

   What is a system of linear equations?

   • A collection of non-linear equations
   • A set of linear equations sharing variables
   • An equation without variables

   Hint

   Think about the equations' nature.

4. 4.

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

   • True
   • False

   Hint

   Consider the meaning of 'inconsistent.'

5. 5.

   Create a system of linear equations that has no solutions, and explain why.

   Hint

   Check if the slopes of the equations are the same.

6. 6.

   Using Gauss elimination, solve the following system: 2x + y = 8 and 3x - 2y = 3.

   Hint

   Set up the augmented matrix and perform row reduction.