Substituting into Expressions

## Substituting into Expressions

An expression consists of numbers and letters. The letters represent numbers for which the values are not yet known.

When the values are known, the letters can then be swapped out for the numbers. This is known as substitution - replacing unknown values with known values.

## Example 1

An expression is shown as 5x + 3y - 2z. If x=3, y=-2 and z=11, what is the value of the expression?

5x + 3y - 2z

Change the letters to numbers

5(3) + 3(-2) - 2(11)

15 - 6 - 22 (watch out for the negative signs)

-13

## Example 2

Here is an expression: 5x^2 - 4y + 3z.

Which gives the greater value -

option A where the values are x=2, y=5 and z=-3 or

option B if the values are x=-3, y=2 and z=-12?

Option A

5x^2 - 4y + 3z

=5(2)^2 - 4(5) + 3(-3)

=20 - 20 - 9

=-9

Option B

5x^2 - 4y + 3z

=5(-3)^2 - 4(2) + 3(-12) (squaring comes before multiplication)

=45 - 8 - 36 (the -3 is squared to give 9, then multiplied by 5)

=1

Answer: Option B (which evaluates to 1. Option A evaluates to -9)