**Recognise When x and y Satisfy an Equation** *KS3 Revision*

## What you need to know

**Things to remember:**

- To see if something “satisfies” something else in maths, it just means to check that it works or is true.
- We use substitution to see if values satisfy an equation.
- If the equation is already in a form that one letter equals everything else, you just need to substitute the other one!

*Does x=4 and y=3 satisfy the equation y=4x-13?*

To see if these values satisfy the equation, all we have to do is substitute them in. We can do this with one of two methods:

**Method 1: **Substitute both numbers in at the same time.

y=4x-13

3=4\times4-13

3=16-13

3=3

It is true that 3 does equal 3, so these values must satisfy the equation! What would happen if, say, x=6?

** **

y=4x-13

3=4\times6-13

3=24-13

3=11

Well, this isn’t right, 3 doesn’t equal 11, so we must know that these values don’t work.

If we go back to our original values, we can try **Method 2,** which we use when the equation has one of the letters by itself.

**Method 2: **If the equation is already in a form so that one of the letters is already by itself, we substitute the other one.

Our equation is already just y= something, so we can substitute x and see if the answer is the same as our original value of y=.

y=4x-13

y=4\times4-13

y=16-13

y=3

This is the same as what we started with, so our values satisfy the equation!

## Example Questions

**Question 1:** *Do x=6 and y=5 satisfy the equation y+2=2x+8?*

y+2=2x+8

5+2=2\times6+8

7=12+8

7=20

7 doesn’t equal 20, so our values don’t satisfy the equaton!

**Question 2:** *Do x=9 and y=12 satisfy the equation y=3x-15?*

*Hint:** We have y=[latex] something, so we can just substitute [latex]x in.*

y=3x-15

y=3\times9-15

y=27-15

y=12

This is what y equalled in the beginning, so these values do satisfy the equation!