# Substitution. How to substitute numbers into expressions.

If you are given an expression and you are asked to substitute certain values into the expression, then you need to change the variables (letters) in the expression to their given values and work out the answer. Substitution is also referred to as plugging. It’s always a good idea to work down the page and not across the page. On the first line of working out substitute your values into the expression and then do any working directly underneath.

**Example **

Substitute the values x = 5 and y = 8 into the following expressions:

a) x + 6

b) x + y

c) 3x + 9

d) 2x + 6y

e) 7x – y

f) 3x² + 2y

g) x - 2y

Answers:

a) x + 6

= 5 + 6 (first substitute your value of x into the expression)

= 11

b) x + y

= 5 + 8 (this time substitute both values for x and y into the expression)

= 13

c) 3x + 9

= 3 × 5 + 8 (this time substitute x into the expression and remember that 3x means 3 multiplied by x).

= 23

d) 2x + 6y

= 2 × 5 + 6 × 8 (this time substitute x and y into the expression)

= 10 + 48 (work out the multiplications first then the addition)

= 58

e) 7x – y

= 7 × 5 – 8 (again both values of x and y need to be plugged into the expression)

= 35 – 8 (work out the multiplication before the subtraction)

= 27

f) 3x² + 2y

3 × 5² + 2 × 8 (again plug in the values of x and y)

3 × 25 + 16 (first square the 5)

75 + 16 (next do the multiplication)

= 91 (finally carry out the addition)

g) x - 2y

= 5 - 2 × 8 (sub in x = 5 and y = 8)

= 5 -16 (work out the multlication before the subtraction)

= -11 (make sure you include the negative sign)

**Example 2**

If z = 2ab + c², work out the value of z when a = 4 b = 10 and c = 9.

All you need to do here is substitute the values of a, b and c to work out the value of z.

z = 2ab + c²

z = 2 × 4 × 10 + 9² (2ab means 2 × a × b)

z = 80 + 81

z = 161

So to recap, substitute means change the letters in the expression or formula to their numerical values. Also set your