## NEKG33 Mathematical methods for economists

## Chapter 3 : Day 03: Equations

### By Lund University

Who doesn't enjoy finding our x? Day 3 is equation day. Remember the pesky formula for solving quadratic equations? We will do this one and some other fun stuff like systems of equations. Lots of stuff today. If overwhelmed, focus on the lectures and get back to exercises when you have the time.

## 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.