Systems of Equations An Introduction

What are systems of equations? A system of equations is a set of two or more equations containing two or more variables. A solution of a system of equations with two variables is the set of ordered pairs that satisfies each equation in the system. (There usually is only one!) We will focus specifically on linear systems in this unit of study!

Different types of Systems The note sheet that you have in front of you describes three different types of systems. Your task is to take notes on the three different scenarios possible when solving a system of equations.

Inconsistent Systems The lines are parallel. equations with no common solutions expressed as: no solution or S = { } – x + y = 3 y = x – 4 The lines are parallel.

Independent Systems linear equations that intersect in just 1 point. Expressed as an order pair in set notation: S = {(x, y)} S = {(2, 3)}

Dependent Systems 2 equations with the same graph infinite number of solutions S={real numbers}

Recall how to solve Solve the systems listed on your note sheet. When you are finished, you should have one example of each system. Remember there are three ways to solve a system…

Solving Systems We will take a look at each of these in class: Systems can be solved by graphing the system of equations. Systems can be solved by substitution where one equation is substituted into the other. Systems can be solved by a process of called elimination. You must eliminate one of the variables. Try either solving by substitution or elimination on the note sheet.

Elimination Elimination (or linearly combinations): process of multiplying 2 variables by constants and adding or subtracting the results. We will call this using linear combinations to solve a linear system or elimination (you will hear both terms used)