How to Solve Simultaneous Equations (PSLE Math Guide)
If your child is aiming for AL1 in PSLE Math, simultaneous equations is one topic they cannot afford to skip.
Many of the most challenging problem sums in PSLE Math involve two unknowns. To solve for two unknowns, your child needs to form two equations and solve them together. That is exactly what simultaneous equations are: two equations solved at the same time.
At Jimmy Maths, we find this is one of the key skills that separates students who score AL1 from those who fall just short. The good news is that with the right method and enough practice, most students can get this down confidently.
In this guide, we will walk through the three main approaches for solving simultaneous equations: the Elimination Method, the Substitution Method, and Model Drawing. Each method comes with a worked example so your child can follow along step by step.
What Are Simultaneous Equations?
Simultaneous equations are a pair of equations that share the same two unknowns, usually written as x and y. The goal is to find the values of x and y that satisfy both equations at the same time.
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.
Example:
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.
Frequently Asked Questions
What are simultaneous equations?
Simultaneous equations are a pair of equations that share the same two unknowns, usually written as x and y. Solving them means finding the values of x and y that make both equations true at the same time.
What is the elimination method for simultaneous equations?
The elimination method works by adding or subtracting the two equations to remove one variable, leaving an equation with only one unknown. It is most useful when one variable already has matching or opposite coefficients in both equations.
What is the substitution method for simultaneous equations?
The substitution method involves rearranging one equation to express one variable in terms of the other, then substituting that expression into the second equation. This leaves one equation with a single unknown, which can then be solved directly.
Can simultaneous equations be solved using model drawing?
Yes. Model drawing is a visual method that works well for primary school students who are not yet confident with algebra. It represents the unknowns as bars or blocks, making the relationship between the two equations easier to see before switching to algebraic methods in secondary school.
Which method should my child use to solve simultaneous equations?
There is no single best method. Full marks are awarded as long as the working is correct and logical, whether your child uses elimination, substitution or model drawing. It is worth practising all three so your child can choose whichever method suits the question best.
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!
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