# GCSE Mathematics/Simultaneous Equations

## Solving simultaneous equations

[edit | edit source]### By elimination

[edit | edit source]One way of solving a simultaneous equation is by canceling out either the x or y values so that you are left with a linear equation.

#### First example

[edit | edit source]In this example, we could subtract the second equation from the first to get this:

Once we know this, we can go back to one of the original equations, and replace y with 5, then solve it, like this:

So, the final solution is:

#### Second example

[edit | edit source]We can see that in this example the equations will not cancel each other out. To make them cancel each other out, we multiply the second equation by two and get:

We can now subtract this from the original equation in order to get a linear equation that we can solve:

Now that we know the value of x, we can substitute it in the first equation in order to solve it:

So, the final solution is: