Simultaneous Equation is a mathematical statement having two (or more) equations and two (or more) of the same unknowns, and are usually solved together.

As usual, in Mathematics the most common variables (letters) used to represent an unknown figure are **X** and **Y.**

Therefore, in this article I will be showing you how to solve Simultaneous equations with two unknowns ( X and Y) using a simple process called the “Elimination” method.

## ELIMINATION METHOD

This method of solving simultaneous equations with two unknowns (X and Y) requires that you first eliminate (cancel off) one of the unknowns (say X) and then solve for the other (say Y).

However, before you can successfully “eliminate” any of the unknowns, you must first make sure that the coefficients (number close to the letters) are equal. That is 2x in the first equation will be able to successfully cancel 2x in the second equation, but -2x won’t do with 2x because 2 and -2 are not equal.

You may want to ask, “How then can they be solved if none of them are equal?”

Don’t fret, just observe the examples below and you will get it in no time.

**EXAMPLE 1**

Solve the Simultaneous equation; 2x + 3y =13, 3x + 3y = 15.

**Solving**:

**Step** **1**— Arrange the equations.

**Step** **2**— Eliminate 3y.

This is because +3y is both equal in equations 1 and 2.

Observe that I circled “minus (-)” on the left side of the equation. This is because only “3 minus 3” can give “zero (0)” which is an “elimination”

**Step 3**— subtract equation (2) from equation (1). This is because of the (minus sign) that eliminated +3y.

That is 2x minus 3x = -x (minus X)

13 minus 15 = -2 (minus 2)

Therefore, -x = -2

**Step** **4**— Divide both sides of the equation by -1 (minus 1), which is the coefficient (the number) of X.

We have successfully gotten the value of X to be **2**.

Now, let us look for Y

**Step** **5**— Substitute the value of X (which is 2) into any of equation 1 or 2.

Here, I choose to use equation (1), and will replace X with 2.

**Step 6**— Make 3y the subject by moving 4 to the right hand side of the equation.

Note: Since 4 is a positive number (+4), it will change to a negative (-4) once it crosses the equality sign.

**Step 7**— Divide both sides of the equation by 3.

We have successfully gotten the value of Y to be 3.

**Check: **We have to see if our answers are correct by using any of the equations 1 or 2. This is done by replacing X with 2 and Y with 3. Here, I choose to check with equation 2.

The answers we got are right. ✔️

## Watch out for part 2…

In The part 2 of this lesson, I will be showing you how to solve simultaneous equations when you can not find equal terms to eliminate. I will also be showing you how to solve questions with complex “sign” combinations.

Until then, Stay Tuned!

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