Simultaneous Equation 1

​Simultaneous Equations

Chapter 9

2x + 4y = 14
4x − 4y = 4

​Example

1. Two equations with 2 variables such as x and y.

2. Find values of the unknowns that satisfy both equations with a solution.

What are simultaneous equations?

​SOLVE SIMULTANEOUS LINEAR EQUATIONS BY  ELMINATION METHOD

​ There are many ways of solving simultaneous equations.

The simplest way is elimination.

This is a process which involves removing or eliminating one of the unknowns to leave a single equation which involves the other unknown.

The method is best illustrated by example.

​Solve the simultaneous equations  
x + 2y = 10   --------  (1)

3x + 2y = 18 --------- (2)

​Solution:      

 

 

​Step 1: Make terms SAME.

​Step 2: Look at sign.
Eliminate SAME terms.

​Solve each pair of simultaneous linear equations using the elimination method.

​Step 1: Make terms SAME.

​Step 2: Look at sign.
Eliminate SAME terms.

​Solve each pair of simultaneous linear equations using the elimination method.

​Step 1: Make terms SAME.

​Step 2: Look at sign.
Eliminate SAME terms.

​Solve each pair of simultaneous linear equations using the elimination method.

​Step 1: Make terms SAME.

​Solution: Eqn 1 X 2:

​Step 2: Look at sign.
Eliminate SAME terms.

​Sub x = 8 in Eqn 1

​Solve each pair of simultaneous linear equations using the elimination method.

​Step 1: Make terms SAME.

​Step 2: Look at sign.
Eliminate SAME terms.

​Two coffees and a tea cost $4.20;

Two coffees and three teas cost $6.60.

How much is each one?

Form 2 linear equations and solve

Draw

Two coffees and a tea cost $4.20;

Two coffees and three teas cost $6.60.

How much is each one?

​ 3 chocolate bars and a mentos cost $1.50;

2 chocolate bars and 2 mentos cost $1.40.

How much is each?

Form 2 linear equations and solve

Draw

3 chocolate bars and a mentos cost $1.50;

2 chocolate bars and 2 mentos cost $1.40.

How much is each?