Algebra - Part 6 - Substitution Method

Equation

a = 3

a has a value of 3

If a + b = 8, what are the values of a and b?

a = 3, b = 5, Check: 3 + 5 = 8

a = 7, b = 1, Check: 7 + 1 = 8

and a lot more answers.

There is no unique solution, because we have two unknowns (a,b) but only one equation (a + b = 8)

Simultaneous Equations

2a + b = 13

3a + 2b = 21

These two equations are called simultaneous equations.

How to find the solution of simultaneous equations?

There are many ways to solve simultaneous equations.  
In this lesson, we will solve by substitution method.

Substitution Method

2a + b = 13 ……..(1)

3a + 2b = 21…… (2)

from (1) we get,

b = 13 – 2a ….(3)

Substituting (3) into (2),

3a + 2b = 21 …..(2)

3a + 2(13 – 2a) = 21

3a + 26 – 4a = 21

26 – a = 21

      – a = 21 – 26 = – 5

         a = 5

b = 13 – 2a 
b = 13 – 2(5)

b = 3