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.