# 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: