## Unit 3 Systems of Equations &

Inequalities

When we are solving a system of equations, we are actually find the intersection point of two lines. Systems of equations can have one solution, no solution, or infinitely many solutions.

Systems with one solution are two lines that intersect in exactly one point. No solutions means that the graphs of the two equations are parallel lines and therefore do not intersect. Systems with infinitely many solutions are coinciding lines. That means that they are the same line

There are three ways to solve systems of equations. They are;

1) Graphing

2) Substitution

and

3) Elimination

Graphing of course is done by graphing two equations and finding the intersection of the two lines. We will begin by graphing these on graph paper and will move on to using the graphing calculator to solve.

Substitution and Elimination are both algebraic methods of solving systems, that is we solve by manipulating the equations and by following a given process, find the solution to the system.

We will begin this unit by reviewing how to rewrite equations into slope intercept form and graph them accurately.

Systems with one solution are two lines that intersect in exactly one point. No solutions means that the graphs of the two equations are parallel lines and therefore do not intersect. Systems with infinitely many solutions are coinciding lines. That means that they are the same line

There are three ways to solve systems of equations. They are;

1) Graphing

2) Substitution

and

3) Elimination

Graphing of course is done by graphing two equations and finding the intersection of the two lines. We will begin by graphing these on graph paper and will move on to using the graphing calculator to solve.

Substitution and Elimination are both algebraic methods of solving systems, that is we solve by manipulating the equations and by following a given process, find the solution to the system.

We will begin this unit by reviewing how to rewrite equations into slope intercept form and graph them accurately.

The next method for solving systems of equations is the Substitution Method. Below is a short video that should help explain how to do this method.

Following that, a short written explanation is on the top of the homework sheet.

Substitution Homework