In this section we will explain step by step the equalizing **method of equalizing** to solve systems of two equations with two unknowns.

There are also other methods of resolution, such as substitution and reduction, but I will focus only on the method of equalizing.

## Method of equalizing step-by-step

Basically, the **method of equalizing** consists of:

- Clear an unknown in one of the equations, which will depend on the other unknown (we will continue to have an equation).
- Clear the same unknown in the other equation
- Equalize the second members of the two unknowns, forming a new equation with an unknown one.
- Clear the only unknown we have left. We get the numerical value of an unknown.
- Replace the unknowns cleared in step 4 with their numerical value in either of the two original equations
- Operate to obtain the numerical value of the other unknown.

Let’s take a slower look at the **method of equalizing** with a resolved step-by-step exercise.

Let’s solve for example the following system of equations:

To know at all times which equation of the system we are referring to, the equation above will be called the first equation and the second equation below:

1- **We clear an unknown in one of the equations**, taking into account the rules of transposition of terms.

The easiest to clear is the “y” in the **first equation**, because it has no numbers in front of it and also has a sign in front of it, so just passing the 5x on the other side and we have the clear one:

2- We clear **the same unknown** in the **second equation**:

3- We matched the second members of the unknowns cleared in steps 1 and 2:

4- Now we have an equation that depends only on x. We’ve cleared it:

5- This value is replaced by, for example, the first equation:

6- And we operate to get the value of y:

Therefore, the solution of this system is x=2, y=-2.

## Method ok equalization : When it should be used

The **method of equalizing** should be used when you have easy to clear the same unknown in both equations. In my view, I always prefer to use the substitution method over the equalisation method, as it is the most widely used.