# GCSE Mathematics/Simultaneous Equations

## Solving simultaneous equations

edit### By elimination

editOne 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

editIn 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

editWe 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: