Week 7: Systems of Equations

We are starting a new chapter, Systems of Equations and Inequalities. The first lesson of the chapter is Systems of Equations. 

This is review from Algebra which is just substitution and elimination. 

There are two tyes of problems in there.

Inconsistent and Consistent.

Incosistent are no solution which are parallel lines or planes

Consistent is the answer which is one solution (independent point) or infinite solutions (dependent line)

To solve Substitution:

1. solve one euqation for one variable

2. substitute into the other equation

3. solve for the variable

4. back substitute to find the second variable

To solve Elimination:

1. Interchange any two equations

2. multiply by a constant number

3. Add one equation to the other to eliminate a variable

It is very simple to solve these types of equations and all you must do is to either substitute or eliminate. 

Here is one problem. 

One problem is when all x, y, and z is equal to 0. That cannot happen. When this happens, you turn z into t and solve for it. 

One example is shown below:

You solve for x with z as t and then so forth.

That’s how you solve systems of equations.

SEE YOU NEXT WEEK!!!