# Simultaneous Equations

## A self-marking, multi-level set of exercises on solving pairs of simultaneous equations.

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7Exam-StyleDescriptionHelpMore

This is level 3: equations that can be added or subtracted to eliminate one variable after both of the equations have been multiplied by constants. You will be awarded a trophy if you get at least 9 correct and you do this activity online.

 3x + 5y = 224x + 4y = 24 x= y= 4x + 5y = 765x + 3y = 69 x= y= 5a + 7b = 626a + 5b = 54 a= b= 3c + 4d = 634c + 3d = 63 c= d= 6e + 6f = 788e − 4f = 8 e= f= -3g − 7h = -15-4g + 5h = 23 g= h= -4j − 11k = -585j − 10k = 25 j= k= 9m + 6n = 6311m − 5n = 114 m= n= -12p − 11q = 13714p − 10q = 0 p= q= -11r + 10s = -5-13r + 9s = -20 r= s= -10u − 12v = -78-11u + 11v = 11 u= v= 12w + 16z = 128-14w + 15z = 19 w= z=
Check

This is Simultaneous Equations level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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#### Tower of Hanoi

Move the pieces of the tower from one place to another in the minimum number of moves. This puzzle was invented in 1883 but is still as captivating today as it was all those years ago.

## Answers

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/software/SW/Starter_of_the_day/Students/Simultaneous_Equations.asp?Level=3

## Description of Levels

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Projectable - A set of simultaneous equations designed to be shown one at a time to the whole class.

Level 1 - Equations that can be added or subtracted to eliminate one variable.

Level 2 - Equations that can be added or subtracted to eliminate one variable after one of the equations has been multiplied by a constant.

Level 3 - Equations that can be added or subtracted to eliminate one variable after both of the equations have been multiplied by constants.

Level 4 - Equations with two variables that are not written in the standard way.

Level 5 - Real life problems that can be solved by writing them as simultaneous equations.

Level 6 - Equations which include fractions in some way.

Level 7 - Linear, quadratic and other pairs of simultaneous equations.

These Level 7 questions will require you to be able to solve Quadratic Equations.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Simultaneous Equations including lesson Starters, visual aids, investigations and self-marking exercises.

## Extension

There is a printable worksheet to go with this activity. It is an exercise that appeared in an algebra book published in 1895. It starts with basic questions but soon gets tricky!

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Level 3 Example

$$7x-2y=3 \qquad \mathbf{A}\\ 2x+3y=33 \qquad \mathbf{B}$$

Multiply equation $$\mathbf{A}$$ by 3 and multiply equation $$\mathbf{B}$$ by 2.

$$21x-6y=9 \qquad \mathbf{C}\\ 4x+6y=66 \qquad \mathbf{D}$$

Add equation $$\mathbf{C}$$ to equation $$\mathbf{D}$$

$$25x=75$$

$$x=3$$

Substitute this value for $$x$$ into equation $$\mathbf{A}$$.

$$21-2y=3$$
$$2y=18$$
$$y=9$$

The simultaneous equations have been solved.
The solutions are $$x=3$$ and $$y=9$$.

You can check your answers by substituting them both into equation $$\mathbf{B}$$ to see if it balances.

This example is not intended to teach you everything you need to know about this type of simultaneous equations. It is here as a reminder and is no substitute for your teacher or tutor.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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