# Math Discussion

Discussion

1.) Suppose that in the process of solving a system of three linear equations in three unknowns, the last row of the matrix contains all zeros. How does this affect the solution of the system of equations?

2.) What are the definitions of the different systems of linear equations: dependent, independent, consistent, and inconsistent?

3.) How many solutions will an independent system have?

4.) How many solutions lie in the solutions region?

A "system" of linear inequalities is a set of linear inequalities that you deal with all at once. Usually you start off with two or three linear inequalities. The technique for solving these systems is fairly simple. Here's an example.

o **Solve the following system:**

**2 x - 3y** <

**12**

<

*x*+ 5*y***20**

*x*> 0

5.) How do you solve the system of inequalities like the one below? Note, this is not a system of equations.

**2x - 3y < 12**

**x + 5y < 20**

**x > 0**

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1) Suppose that in the process of solving a system of three linear equations in three unknowns, the last row of the matrix contains all zeros. How does this affect the solution of …