Substitution

Video 1

Video 2

Substitution is not hard at all, it is just substituting the letters with a given number.
When we solved for x, when working out linear equations, we found out what x equalled.
Lets say the linear equation we need to solve is 2x + 3 = 7, we know x = 2. To show x = 2 lets substitute x with 2 in 2x + 3 = 7.
So 2(2) + 3 =7
4 + 3 = 7
THIS IS SUBSTIUTION.

Video 1 Explanation

Question:
If f(x) = 2x + 10 + x, find the value of the function when x = 2
To answer this we must substitute x = 2 into 2x + 10 + x
f(2) = 2(2) + 10 + (2) = 4 + 10 + 2 = 16
so f(2) = 16
So when x = 2, the function's output is equal to 16.
Lets try another question with the same function.
What value does the function take when x = 34
f(34) = 2(34) + 10 + 34 = 68 + 10 + 34 = 112
So when x = 34, the function's output is equal to 112.
f(x) is the notation for a function with input x. The input x is substituted with numbers like we did before, when we substituted x with 2 and 34.
Once we input a number into the function, we attain an output, when we inputted 2 into the function we attained 16 as the output and when we inputted 34 into the function, we attained 112 as the output.
So a function has an input x, which we substitute with numbers to obtain an output.

Video 2 Explanation

Question:
If y = 3x + n² + 2n, what does y equal when x = 3 and n = 5.
In this question we have two inputs, this is x and n. So lets now substitute x = 3 and n = 5 to find y.
y = 3(3) + (5)² + 2(5) = 9 + 25 + 10 = 44
y = 44
This question had 2 inputs (n and x), however, you could also get a question with more than 2 inputs.
Lets try a question with three inputs.
If s = (a² -c²)/(2ad), find the value of s, when a = 3, c = -5, d = 1. Give your answer to 1 decimal place.
Lets now substitute the values to find s.
s = (3² - (-5²))/(2 x 3 x 1)
s = (9 - 25)/(6)
s= (-16/6)
s = -16/6 = -2.67

Substituting letters for non-numbers

Substituting the letters in expressions with numbers is not the only way we can substitute, however if you can substitute numbers for letters in the expression, you can understand the following questions, as how you substitute remains the same.
Question 1: Substitute x with (a + b) in the expression x + a + 5
a + b is an expression itself, so the questions tells us that we need to substitute x with (a + b), therefore x = a + b
x + a + 5 = a + b + a + 5 (WE CAN SIMPLIFY THIS BY COLLECTING LIKE TERMS)
a + b + a + 5 = 2a + b + 5

Try these questions

Let f(x) = 2x² + 3x - 5, Find f(2), f(3) and f(4)
s = 2ab + 3ab + 4c, find the value of s when a = -1, b = 2 and c = 7

Answers

f(2) = 2(2²) + 3(2) - 5 = 2(4) + 6 - 5 = 8 + 6 - 5 = 9

f(3) = 2(3²) + 3(3) - 5 = 2(9) + 3(3) - 5 = 18 + 9 - 5 = 22

f(4) = 2(4²) + 3(4) - 5 = 2(16) + 12 - 5 = 32 + 12 - 5 = 39

s = 2ab + 3ab + 4c = 5ab + 4c (We can simplify by collecting like terms)

s = 5(-1)(2) + 4(7) = -10 + 28 = 18

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