# How to solve simultaneous equations using the elimination method in WAEC & JAMB : Nigerian Education Simultaneous equation is a fairly easy math to solve if you are familiar with the prescribed formula. Note that there are two methods of solving simultaneous equations, either in WAEC, NECO, JAMB, or in an exam or test you are trying on this topic.

Simultaneous equation is one of the most common topics in mathematics for which the West African Examination Council, WAEC, tests candidates each year. You will see it either as an objective question or as a theoretical question and sometimes it can appear in both sections.

If the simultaneous equation appears in the “Theory” section, you will most likely need to answer the question using the graphical method, as the body wants to test your deep understanding of this mathematical subject. Don’t worry, we’ve broken down the steps to graphically solving the simultaneous equation. This would help candidates or students achieve full marks for the question in the long run. In this post, I will walk you through the simple and complete breakdown of solving simultaneous equations using the elimination method.

Ideally, there are two methods for solving simultaneous equations.

1. Graphic method
2. Algebraic methods (substitution and elimination)

I will give some examples of how to solve simultaneous equations The elimination method.

Example 1:

2x + 3y = 12 – (1)
5x + 2y = 8 – (2)

First we look for a way to eliminate either the x variable and the coefficient (2.5) or the y variable and the coefficient.) (3.2).

To eliminate either the x or the y variable, we make sure that they have the same values. Now let’s remove the x variables so y stands for itself. The only way to do this is to take the coefficient of x, which is in equation (2) 5, and multiply it by the whole of equation (1), and also to take the coefficient of x, which in equation (1) is 2. multiply it by the entire equation (2).

5 2x + 3y = 12 ___ (1)
X.
2 5x + 2y = 8 ____ (2)

We multiply equations (1), (2) by 5 and 2….

:. We have;

10x + 15y = 60 ____ (3)
10x + 4y = 16 ____ (4)

Now we can safely eliminate x variables and coefficients.

:. 10x-10x + 15y-4y = 60-16

:. 15y – 4y = 60 – 16
:. 11y = 44
We divide both sides by 11 so you are alone

:. (11y) / 11 = 44/11

:. y = 4

Example 2;

4x – 2y = 10
x + y = 4

Multiply x + y = 4 by 2 to get 2x + 2y = 8

4x – 2y = 10
2x + 2y = 8
6x = 18
x = 3

You need to add the two equations that “eliminate” the 2y (since -2y + 2y = 0) and 6x = 18, which results in dividing both sides by 6 x = 3

Therefore; 3 + y = 4
y = 1

Then replace x in one of the equations with the value 3. (In this example this is easier in x + y = 4 than in 4x – 2y = 10)

4x – 2y = 10
(4 x 3rd) – (2 x 1) = 10
12 – 2 = 10

After getting your x and y variables, always check the correctness of your solution by checking the values ​​for x and y in the other equation.

Did you just understand that? If you have any questions about how best to solve the simultaneous equation using the WAEC elimination method or an exam, please contact us via the comments section below and we will respond accordingly.  