# SIMULTANEOUS LINEAR EQUATION

OBJECTIVE:

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

(1) identify simultaneous pair of linear equation;

(2) solve simultaneous linear equation by substitution method.

CONTENTS:

* Define simultaneous linear Equation,

* Methods of solving simultaneous linear equation,

* Simultaneous linear equation using substitution  method.

DEVELOPMENT: Simultaneous linear equation is a pair of linear equations that involves two unknowns and  the order of unknown is one.

Example of simultaneous linear equation is as follows:

3a + b = 10 and 2a + 4b = 0

There are three different methods of solving simultaneous linear equation, namely:

(1) Substitution method,

(2) Elimination method and

(3) Graphical solution method.

SUBSTITUTION METHOD.

Substitution simply means to put something in place of another. Method of substitution is mostly applicable when the coefficient of one of the unknowns in the given equation is one.

Example1: Solve the equations 3a + b = 10 and 2a + 4b = 0.

3a + b = 10—–(1)

2a + 4b = 0——(2)

From equation(1) above b = 10 – 3a, then substitute b = 10 – 3a in equation (2).,

Thus: 2a + 4(10 – 3a) = 0.

Clear bracket and collect the like terms.

2a + 40 -12a = 0

-10a = -40

Divided both sides by -10.

a = 4.

Substitute 4 for a in equation (1) above now.

3(4) + b = 10.

12 + b = 10.

Then, b = 10 – 12

b = -2.

a = 4, b = -2 is the solution of the two unknowns in the equation.

Example2: Solve the below pair of simultaneous equation

y = x + 1 and x + y = 3.

Solution:

y = x + 1—-(1)

x + y = 3—–(2)

From equation (1) above y = x + 1, then substitute y = x + 1 in equation (2).

x + (x+1) = 3 .

Clear the bracket and collect the like terms.

x + x + 1 = 3.

2x = 3 – 1

2x = 2

Divided both sides by 2

x = 1.

Substitute x = 1 in equation (1).

y = 1 + 1

y = 2

Thus: x = 1, y = 2.

ELIMINATION METHOD

When none of the coefficient  of the unknowns is one, then use of elimination method  is essential. This method is to get rid of one of the unknowns, by making the coefficient of one of the unknown ryhme in the two equation. Then add or subtract the equations as necessary.

Example 3: Solve  the equations

3x + 2y = 12 and 5x – 3y = 1.

Step_1: Elimination

Make the coefficient of y the same by multiplying equation (1) by 3 and equation (2) by 2

9x + 6y = 36

10x – 6y = 2

Add up the two equation. Then arrived at.

19x = 38.

x = 2.

Step_2; Subtitution

Substitute 2 for x in equation (1) above.

3(2) +2y = 12

2y = 12 – 6

y = 3

Thus, x = 2 and y = 3.

ASSIGNMENT: Solve the below pairs of simultaneous linear equations by substitution method.

(1) a = 5 – 2b and 5a + 2b = 1.

(2) x + y = 4 and 2a + 3b = 4.

(3) Solve the below pair of simultaneous equation by elimination.

5x +2y = 2y and 2x + 3y = -8.