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# 2 Methods To Solve Tricky Simultaneous Equations Questions in Secondary Mathematics

Updated: Jun 20, 2023

As your secondary school child delve deeper into their Secondary Math studies, they may encounter the challenging world of Simultaneous Equations. These equations contain multiple variables, and solving them can be pretty tricky. However, fear not!

In this blog post, we'll share 2 methods to help your child quickly solve these equations. We'll cover the Substitution Method and Elimination Method, as well as tips for the above methods. With these tips in mind, your child can confidently tackle even the most complicated simultaneous equations problems.

So let's dive in and explore the world of Simultaneous Equations questions!

## What are Simultaneous Equations?

Simultaneous Equations are two or more algebraic equations that share variables e.g. x and y. The goal is to find the values of x and y that make both equations true simultaneously.

Think of it as solving two puzzles at once! They are called simultaneous equations because the equations are translated at the same time.

## Methods to Solve Tricky Simultaneous Equations Questions

### Method 1: Substitution Method

The Substitution Method is a technique used to solve systems of equations in which one variable is solved for in terms of another variable in one of the equations and then substituted into the other equation(s) to solve for the remaining variable(s).

Tip: Isolating a Variable

The goal of the substitution method is to isolate one of the variables in one equation and then substitute that expression into the other equation, thereby reducing the expression to a single equation in one variable that can be solved.

Step 1: Look for a variable that is easy to isolate. In the case below, the variable is y in the first equation.

Step 2: Make the selected y the subject.

Step 3: Sub this equation into the second equation. As shown in the picture below. Then you solve for x, as per usual.

### Method 2: Elimination Method

The Elimination Method is a technique used to solve systems of equations by adding or subtracting the equations to eliminate one of the variables. The resulting equation will have only one variable, which can then be solved to find its value. This process is repeated for the other variables until all variables have been solved.

Step 1: Ensure the coefficients of the variables are opposite. For example, look at the y variable below in the first 2 equations.

Step 2: We add the equations together and solve for the x variable, as shown below.

Tip: Grouping Like Terms Together

Grouping like terms together is a technique used to simplify and solve equations multiple times. A general tip for solving simultaneous equations is to group like terms together to simplify the equations in such a way that only different terms are left in each equation. This has to be done before solving simultaneous equations using either Substitution Method or Elimination Method.

This helps to make the equation easier to work with and solve. By combining like terms, you can reduce the number of terms in an equation and make it easier to identify the value of each variable.

Step 1: When there are many terms, first group all the like terms together. This will ensure you solve the equation more easily.

An example is shown below.

Step 2: The equations will look less complicated after combining similar terms.

Step 3: Now you can easily see that the term containing "z" can be easily removed when the 2 equations are added together.

Solving simultaneous equations questions can be challenging, but with the proper techniques, it can become easier and more manageable. Using the Substitution Method and the Elimination Method, your child can confidently tackle any simultaneous equations problem that comes their way.

As parents, you can support your children in their Secondary Math studies by encouraging them to practice these techniques regularly and seeking help from their teachers or tutors when needed. With these tips, your child can develop their Secondary Math skills and become more confident in solving tricky simultaneous equations questions.

At AGrader Learning Centre, students get to practise a variety of hard simultaneous equations questions that are commonly tested in exams. With our educators' guidance, students get exposure to simultaneous equations practice questions and learn techniques to solve them efficiently. We equip secondary students with the necessary skills to solve even the most challenging Secondary Math practice questions by providing top-quality study materials and worksheets curated by our experienced educators in the Secondary Math Tuition Programme.

Take your childâ€™s Secondary Math skills to the next level. Enrol them now at AGrader Learning Centre's Secondary Math Tuition Programme.