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Algebra Substitution for the 11 Plus Exams

1. What is Substitution in Algebra?

Substitution means replacing. In algebra, when we replace a variable with a number, we call it substitution. 

For example, consider the expression 2x + 3. 

Let us assume x = 2. So to substitute x, replace it with 2. When we do this replacement, we can write 2 × 2 + 3.

Note when we substitute a variable, we must always follow the order of operations (BIDMAS or BODMAS) rule to calculate the value after substitution. 

Hence, 2 × 2 + 3 = 4 + 3 = 7.

1.1 Example Questions on Substitution

Example 1: If a = 2, b = -1 and c = 1 find 2a - 4b + 5c²

Solution : Substituting a, b and c with their values we get, 

                2a - 4b + 5c²  = 2 × 2 - 4 × (-1) + 5 × 1²

                Following BIDMAS rule, 

                = 2 × 2 - 4 × (-1) + 5 × 1             (first calculate Indices)   

                = 4 + 4 + 5                                    (then multiplication)

                = 13                                               (then addition)

Example 2: Equation to convert fahrenheit (F) to Celsius (C) is given by:

                   F = 9⁄5 × C + 32 

                   Work out the temperature in Fahrenheit if C = 35.

Solution:  Substituting C = 35 in the equation we get, 

                F = 9⁄5 × 35 + 32                     

                Following BIDMAS rule,

                F = 9 × 7 + 32                        (First division)

                F = 63 + 32                             (then multiplication)

                F = 95                                     (then addition)

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