Lesson 1: Elimination method

Objectives

At the end of the lesson, students should be able to:

• Know the two most common ways of solving simultaneous equation.

• Use the elimination method to solve equations simultaneously.

The process of solving two equations and finding a common solution is known as solving equations simultaneously. You will be given a pair of linear equations for which you want the same solution and which you therefore solve together. For example, the equation x + y = 8   has many solutions:

The two most common ways of solving simultaneous equations algebraically are elimination method and substitution method.

Elimination method: The aim of this method is to eliminate one of the unknown variables by either adding or subtracting the two equations. There are six steps in this method.

STEP 1: Balance the coefficients of one of the variables.

STEP 2: Eliminate this variable by adding or subtracting the equations.

STEP 3: Solve the resulting linear equation in the other variable.

STEP 4: Substitute the value found back into one of the previous equations.

STEP 5: Solve the resulting equation.

STEP 6: Check that the two values found satisfy the original equations.

Example 1

Solve the equations:
4x + y = 23
x + y = 8

Solution

Label the equations:

4x + y = 23 ………………… (1) 
x + y = 8 ……………………. (2)

STEP 1:

Since the y-terms in the equations have the same coefficient, there is no need to balance them.

STEP 2:

Eliminate y by subtracting equation (2) from equation (1).

These are correct, so you can confidently say that the solution is
x = 5 and y = 3.