# Simultaneous linear equations

## Introduction

In your previous unit you dealt with linear equations.You will also recall that these equations are of the first degree and their graphs are straight lines.We are moving further to simultaneous linear equations.These types of equations are like linear ones of the first degree but with two or more unknowns.

Objective
 By the end of this unit you should be able to identify simultaneous equations, solve simultaneous linear equations by both the substitution and elimination methods. formulate word problems into simultaneous linear equations and solve them.

## Lesson content

Now consider the following equations;

• 2f+1=23
• 4(a-3)=16

 2x-y=6 x+y=5

 5x+2y=3 2x+3y =-1

Do you notice any similarities and differences among the equations?You will see that the first two have just one unknown and the last two are in pairs having two unknowns.The first two are linear equations and the paired ones are called simultaneous linear equations. How do solve these equations? you can solve them the methods of either substitution,elimination or graphically. Let us examine the substitution method.There are three points to note

1. make one of the unknowns or variables the subject of the other in one of the equations.
2. substitute the expression into the other equation to find the unknown.
3. Find the other unknown by substituting the value got in point 2 into the original equation.

# Example

 2x-y=7 x+y=2

make x the subject

 2x-y=7 x+y=2 _____
3x=9