Can you think of an instance when substitution is done? In a basketball game, a better player usually replaces a player who does not perform well, or maybe one player needs some rest so another player has to come in. Replacing one player by another player is called substitution. In Algebra, we replace a variable with a number. This is called substituting the variable. To evaluate an algebraic expression, substitute the variable by a number and simplify the expression. Evaluating an algebraic expression means obtaining or computing the value of the expression where value/s of the variable/s is/are assigned.
Illustrative example 1
Evaluate 2y + 3 when y = 3
Solution: = 2(3) + 3 Substituting y by 3
= 6 + 3 Multiplying 2 and 3
= 9 Adding 6 and 3
Illustrative example 2
Evaluate 3(a + 4) + (a – 2) when a = 6
Solution: = 3(6 + 4) + (6 – 2) Substituting a by 6
= 3(10) + 4 Computing 6 + 4 and 6 - 2
= 30 + 4 Multiplying 3 and 10
= 34 Adding 30 and 4
Illustrative example 3
Evaluate 2(x + 4) + 3(y – 3) when x = - 3 and y = 5
Solution: = 2(-3 + 4)+3(5–3) Substituting x by 4 and y by 5
= 2(1) + 3(2) Computing -3 + 4 and 5 - 3
= 2 + 6 Computing 2(1) and 3(2)
= 8 Computing 2 + 6
Illustrative Example 4
Evaluate (2x ÷ 3) - 2y + 2y2 when x = - 6, y = 3
Solution: = [2(-6)÷3]-2(3)+2(3)2 Substituting x by –6 and y by 3
= [-12 ÷ 3] - 6 + 2(9) Computing 2(-6); -2(3) and (3)2
= - 4 - 6 + 18 Computing -12 ÷ 3 and 2(9)
= 8 Computing – 4 – 6 +18