System of Linear Equations

Chapter2Section3

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with two variables. The solution to this system is the point of intersection - the shared point (x,y).

There are several methods for finding this point of intersection:

Graphical Substitution Elimination

Graphical Solutions

The graphical method for solving systems of equations is the same method use in Section 2.1. The point of intersection of the two equations is the value of x and y that satisfy both equations simultaneously.

Example 1

Solve graphically:

From the graph you can see the point of intersection (0.5, -5700). This means that when x = 0.5, the y value is -5700.

Graphing as a means of solving is not as accurate as the other methods we will discuss.

A Business Model

The two equations that make up the system are:

A Business Model

Find the point of intersection on your graphing utility.

The solution is the point (12, 67,020).

Example 2

First, solve each equation for the function. Then graph.

Substitution

Example 3

Example 4

Market equilibrium occurs when the supply quantity equals the demand quantity. If the price results in more units supplied than demanded, its called a surplus. If the price results in less units than demanded, its called a shortfall. Answer the following for the system where q is the number of units demanded and p is the price per unit. demand

supply

Elimination

Example 5

Modeling Systems of Linear Equations

Types of Solutions

Example 8