Recognise When x and y Satisfy an Equation | KS3 Maths Resources

## 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!

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## Example Questions

$$y+2=2x+8$$

$$5+2=2\times6+8$$

$$7=12+8$$

$$7=20$$

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

Hint: We have $y= something, so we can just substitute x$ 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!

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