How to Solve Simultaneous Equations

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We can solve an equation with one unknown. By rearranging the equation 2x + 3 = 11 for instance, we are able to find the unique value of x for this equation to be true. Can we solve an equation with two unknowns? What are the unique values of x and y in the equation 2x + y = 7? When we have two unknowns/variables, we need two equations in order to find the variables' values. We have three strategies to do so successfully and you need to be able to use all three of them;

- the substitution
- the elimination method
- the graphical method.

I will explain all methods here to solve simultaneous equations. So continue with your maths revision and make sure to study all maths videos and example questions. Good luck and have fun!

The Substitution Method: How to solve Simultaneous Equations

It is unfortunately my experience that most student regard the substitution method to be complicating and confusing. I am convinced however that everybody, including you, will understand this important mathematical strategy when it is given a proper try. The maths skills and understanding which you will develop while performing the substitution method, will not only be used when solving simultaneous equations, but you can use them for all types of questions in the future. So give the following videos your full attention and try to have some fun at the same time! Good luck!!

Strategy:

- Choose a variable from one equation and make it the subject
- Substitute that in the other equation
- Solve the equation
- Substitute your found value of the variable in one of the equations and solve for the other variable
- Check your answers by substituting them both in both equations

Huh?! Have a look at the videos!!

Example questions solving Simultaneous Equations with the Substitution Method

In the following two videos I will solve the same question using a slightly different approach the second time. You will benefit from having a range of strategies to solve problems which will further develop your understanding. This will allow you to solve these questions too when they are slightly differently asked or placed into a new context in the future.

Two more videos which will solve simultaneous equations by substitution. In video two I will again take a slightly different route compared to what I did in the first video. Study both during your maths revision for the more example questions you try, the better you will understand maths!

The Elimination Method: How to solve Simultaneous Equations

By adding or subtracting the equations we can also solve simultaneous equations. We call this the elimination method and most students prefer this method above the substitution method. Be careful however for there are quite some things you need to consider when applying the elimination method. Have a proper look therefore at all videos below which will discuss everything you need to take into account to be successful.

Strategy:

- Make sure your x's, y's and numbers are nicely aligned
- Decide which variable to eliminate
- Decide whether one or both equations need to be multiplied by a particular factor
- Add or subtract the equations (use your maths finger!!)
- Solve for the variable which has not been eliminated
- Substitute your found value in one of the other equations
- Solve for the other variable
- Check your answers by substituting them both in both equations

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Example questions how to solve Simultaneous Equations with the Elimination Method

There are several things you need to consider when applying the elimination method. Make sure therefore to look at all example questions which will study all those things you need to be aware of in order to be successful. Each video will contain something new for you to think about and understand. Remember, the best way to learn and understand maths is by solving these types of example questions. Good luck and have fun!

Do you already understand how to solve simultaneous equations? Then try this last example question and find out whether you can move on to solving simultaneous equations graphically or whether you need more help with your maths!

The Graphical Method: How to solve Simultaneous Equations

So far I have explained to you how to solve simultaneous equations by substitution and by using the elimination method. Finally I will teach you how to solve simultaneous equations by graphing the equations. Which method do you think is most accurate? Please share your thoughts on the forum of this website and start the discussion!

Strategy:

- Graph both equations
- Find the point of intersection of the two lines
- The coordinate of the point of intersection is your solution

Example questions how to solve Simultaneous Equations with the Graphical Method

The best way to learn maths is by solving example questions yourself. Have a look therefore at the following videos during your maths revision and try to answer the questions. Check my explanation and answer later and check whether you understand how to solve simultaneous equations graphically or whether you need more help with your maths. Good luck!

Solving a Past Paper Question about Vectors and Simultaneous Equations

One of you asked for my help solving this Past Paper Maths Exam Question. Are you prepared to pass your IGCSE GCSE Maths exam and can you solve this question? Good luck and have fun!!

Congratulations!! You now understand how to solve simultaneous equations! You have learned what the substitution and elimination method are and you understand how to solve simultaneous equations graphically. Continue with your maths revision and learn about how to solve inequalities. Do you approach them the same as equations? Find out by following the links. I will see you there!!

How to solve Inequalities