Substitution into an Algebraic Expression

Substitution into an algebraic expression is the process of replacing a letter with a number, in a given algebraic expression. The letters are called variables because they can be replaced by any value.

Example 2.4.1:

If  x =  2  and y  =  3    

Find the following:

i. \( \scriptsize x \: + \: 6 \)
ii. \( \scriptsize 4 \: + \: x \: + \: y \)
iii. \( \scriptsize y \: – \: x \)
iv. \( \scriptsize 10 \: – \: 2y \: – \: 3 \)

Solution

i. \( \scriptsize x + 6 \\ = \scriptsize 2 + 6 \\ = \scriptsize 8 \)

ii. \( \scriptsize 4 + x + y \\ = \scriptsize 4 + 2 + 3 \\ = \scriptsize 6 + 3 \\= \scriptsize9 \)

iii. \( \scriptsize y \: – \: x \\ = \scriptsize 3 \: – \: 2 \\ = \scriptsize 1 \)

iv. \( \scriptsize 10 \: – \: 2y \: – \: 3 \\ = \scriptsize 10 \: – \: 2(3) \: – \: 3 \\ = \scriptsize 10 \: – \: 6 \: – \: 3 \\ = \scriptsize 10 \: – \: 9 \\= \scriptsize 1\)