## Mathematics for Economists

## Chapter 3 : Equations and sums

### By Lund University

Most of chapter 3 is devoted to equations but we have also included a section on the summation sign. We will introduce all the terminology that we need for a fundamental understanding of what it means to solve an equation. We will focus most of our attention on quadratic equations and systems of linear equations.

## Equations: Rules and terminology

In this section, we will look at the basic terminology for equations and the rules that you can use to solve equations. We will look at the distinction between a variable and a constant in an equation and we will learn how to classify an equation allowing us to apply the appropriate methods to solve the equation.

#### Equivalent equations and inequalities

#### Equations, terminology

#### Equations, constants and variables

#### Classification of equations

#### Solving equations

## Quadratic equations

Quadratic equations is an important class of equations. We will review the formula for solving a general quadratic equation and a reduced quadratic equation (which is a quadratic equation where the constant in front of the x-square term is one). In this section we will also look at how to factor a quadratic expression and learn how to completing the square of a quadratic expression.

#### Reduced quadratic equations

#### Quadratic equations

#### Factoring a reduced quadratic expression and completing the square

#### Factoring a quadratic expression and completing the square

## Single equations: Problems

Exercises on quadratic equations and other equations

#### Problem: Solve linear and quadratic equations

#### Problem: Understanding the quadratic formula

#### Problem: Solve linear and nonlinear equations

#### Problem: Simplify by factoring

#### Problem: Solve equations

#### Problem: Factor expressions

#### Problem: Solve inequalities

#### Problem: Solve text-equations

#### Problem: Solve equations containing constants

#### Problem: Solve equations containing constants

#### Problem: Solve quadratic equations

#### Problem: Solve quadratic equations

#### Problem Solve quadratic text-equations

#### Problem: Solve equations containing square roots

## Systems of linear equations

This section is an introduction to systems of linear equations. We will restrict the study to two linear equations and look at two methods for solving such a system. The first method is called the substitution method and the second is the elimination method.

#### Systems of equations

#### Problem: Solve systems of equations

#### Problem: Solve systems of equations

#### Problem: Solve systems of equations

#### Problem: Solve non-linear equations

## Sums and the summation sign

The final section of this chapter is not really about equations but it could not find a better home. Here, we will look at the summation sign and the rules that you can use to simplify expressions using the summation sign. These rules are not new, they are the same rules that we met in chapter 2, such as the distributive law. However, in chapter 2 we only considered the sum of two elements. We need to extend this to sums of an arbitrary number of elements.