21.1.3. Solution Methods

Try these first

1. 1.

   Describe the graphical method of solving a system of equations.

   Hint

   Think about how you visualize equations on a plane.

2. 2.

   What is the outcome if lines in a system are parallel?

   Hint

   Consider what parallel lines represent.

3. 3.

   Which method is best for solving large systems of equations?

   • Graphical Method
   • Substitution
   • LU Decomposition
   • Elimination

   Hint

   Think about which method is computationally efficient.

4. 4.

   True or False: A consistent system can have infinitely many solutions.

   • True
   • False

   Hint

   Recall the definitions of consistent and dependent systems.

5. 5.

   A system of equations has two equations: 4x - 2y = 8 and 2x + y = 5. Show all steps to find the solution using both substitution and elimination methods, and compare results.

   Hint

   Start with the easier variable to isolate.

6. 6.

   Using Gauss elimination, solve the following system: x + 2y + z = 7, 2x + 3y + 4z = 12, 3x + y + z = 10. Provide a complete breakdown of the elimination steps.

   Hint

   Focus on the step of eliminating one variable at a time.