You can solve simultaneous equations by adding or subtracting the two equations in order to end up with an equation with only one unknown value.

This is known as the **algebraic method**.

Solve the simultaneous equations:

**(1)**

**(2)**

Add the two equations together and you will find that the disappears:

This can be simplified to:

Substituting this value of in **(1)** gives:

Check in **(2)**:

(which is correct)

So the solution is:

,

- Question
Solve the simultaneous equations

Firstly use labels for the equations:

**(1)****(2)**To make the s disappear we can subtract equation

**(2)**from equation**(1)**:This simplifies to:

Substitute in

**(1)**:Check in

**(2):**(which is correct)

So the solution is:

,

Sometimes equations need to be altered, by multiplying throughout, before being able to eliminate one of the variables (letters).

Solve the simultaneous equations:

**(1)**

**(2)**

Neither the nor the will be eliminated by adding or subtracting these equations as they stand.

By multiplying the second equation by throughout, both equations will then include , which will allow us to continue with the solution.

**(2)** gives **(3)**

Don’t forget to multiply the right hand side by as well.

Now, looking at equations **(1)** and **(3)**, as they both include ‘ ’, we will subtract one equation from the other.

Subtract equation **(1)** from equation **(3)** and you’ll find that the disappears:

This can be simplified to:

Substituting this value of in **(1)** gives:

Check in **(2)**:

(which is correct)

So the solution is:

,

- Question
Solve the simultaneous equations:

Firstly use labels for the equations:

**(1)****(2)**To make the s disappear we need to multiply equation

**(2)**by before adding to equation**(1)**:**(2)**gives**(3)**By adding equation

**(1)**and equation**(3)**and you will find that the disappears:This can be simplified to:

Substitute in

**(1)**:Check in

**(2)**:(which is correct)

So the solution is:

,