# Section 2.1

## Systems of Linear Equations

In Chapter 1, we looked at several applications of linear functions. One set of linear functions was the cost and revenue functions for a dairy. These functions can be analyzed to determine when the dairy farm is making money and when it is losing money. The break-even point is the point at which a farm’s costs are equal to its revenue. In this section we’ll learn how to find this point graphically.

We also looked at supply and demand functions for milk. These functions model the consumer’s and supplier’s behavior with respect to the quantity and price of milk in a market. In economics, we are interested in knowing how the quantity of milk sold is related to the price of milk. The equilibrium point describes the price of a commodity, such as milk, when the quantity demanded by consumers matches the supply that manufacturers are willing to provide. In this section we’ll locate the equilibrium point graphically.

For both of these applications, we need to find a point of intersection of two lines. Many other applications require the same mathematical process. At the end of this section we’ll build an application from the ground up. In this application, we’ll learn how different types of gasoline containing ethanol can be blended together to yield a mixture with a particular volume and level of ethanol. 