How to Solve Simultaneous Equations

How to Solve Simultaneous Equations

It has been said that “If your child wants to score AL1 for PSLE Math, he must know how to solve Simultaneous Equations.”

Someone also told me that the ability to solve Simultaneous Equations is what differentiates the ‘AL1’ students and ‘A’ students. To a certain extent, I think it is true. Most of the challenging problem sums in PSLE Math has 2 unknowns. To solve for 2 unknowns, you need to create 2 equations and solve them at the same time. That is we call them Simultaneous Equations.

Solving Simultaneous Equations is an important skill to solve challenging questions in PSLE Math papers.

There are 2 popular methods to solve Simultaneous Equations: The elimination Method and the Substitution Method

Elimination Method

We use the elimination method to eliminate one of the variables.

The elimination method is used when the values of the coefficients of one variable in both equations are the same. [Coefficient = Number in front of the variable]

Example of the Elimination Method

3x + 7y = 38  – (1)
3x + 6y = 33  – (2)

In this example, we notice that the coefficients of x are the same in both equations (3x = 3x).

Hence, we use equation 1 minus equation 2 to eliminate x to find the value of y.

(1) − (2):

7y − 6y = 38 − 33

y = 5

Next, we use the value of y to substitute into either of the equations to find the value of x.

3x + 7 x 5 = 38

3x + 35 = 38

3x = 3

x = 1

Substitution Method

In this method, we first rearrange one equation to express one variable in terms of the other variable.

Next, we substitute this expression into the other equation to obtain an equation in only one variable.

Example of the Substitution Method

4x + y = 11   – (1)
7x + 2y = 20  – (2)

From the first equation, we can rearrange the equation to make y in terms of x and label this as Equation 3.

y = 11 − 4x  – (3)

Next, we substitute Equation 3 into Equation 2 to obtain one equation in x only.

7x + 2(11 − 4x) = 20

7x + 22 − 8x = 20

x = 22 − 20

x = 2

Now, we can substitute the value of x into Equation 3 to find the value of y.

y = 11 – 4 x 2

y = 3

Can My Child Use Model Drawing to Solve Simultaneous Equations?

Yes, your child can also use Model Drawing to solve Simultaneous Equations!

Model drawing is great for visual learners. As primary school students’ minds are still not trained to handle complex Algebra yet, model drawing maybe more appealing for them.

Nonetheless, Algebra is a must-know skill as you will be learning how to use Algebra to solve more complicated equations in Secondary Math. That is why I strongly encourage primary school students to pick up Algebra well.

I shall go through how to solve Simultaneous Equations using Models and Algebra. Watch the 2 videos below to learn how.


Ahmad and Bernard had a total of  $240. Ahmad spent 2/3 of his money and Bernard spent 3/5 of his money. As a result, Bernard had $8 more than Ahmad. How much did they spend altogether?


Using Model to Solve Simultaneous Equations



Using Algebra to Solve Simultaneous Equations


After watching the videos, which method do you prefer?

Many students also ask me, “Which method is better?”

Either one is fine as long as you know how to apply it correctly. Marks will be awarded as long as your workings are logical. In fact, you may have other methods instead of Model and Algebra. 

These methods are covered more in-depth in my online course. More details can be found below. 

8 Must Know Methods to Solve Problem Sums - Online Course

Don't go for exams with knowing these 8 methods! They are crucial!

8 Must Know Methods for PSLE Math

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