# Simultaneous Equations

## A self marking exercise requiring you to solve a pair of simultaneous equations.

##### Level 1Level 2Level 3Level 4Level 5Level 6ProjectableDescriptionHelpMore

This is level 6; Equations which include fractions in some way. You can earn a trophy if you get at least 9 correct. Show all of your working in your exercise book.

 $$3x + \frac{y}{2} = 21 \\x + \frac{y}{3} = 10$$ x= y= $$5x + \frac{y}{3} = 50 \\ \frac{x}{2} + 3y = 94$$ x= y= $$7a + \frac{b}{2} = 34 \\4a + \frac{b}{4} = 18$$ a= b= $$\frac{c}{2} + \frac{d}{3} = 19 \\\frac{c}{4} + \frac{d}{5} = 11$$ c= d= $$\frac{e}{3} + \frac{f}{2} = 29 \\\frac{e}{2} - \frac{f}{3} = -2$$ e= f= $$\frac{g}{3} - \frac{h}{5} = 14 \\\frac{g}{7} + \frac{h}{4} = 53$$ g= h= $$\frac{j}{3} = 22 - \frac{k}{2} \\\frac{j}{2} - \frac{k}{3} = 7$$ j= k= $$\frac{m}{3} - 27 + \frac{n}{2} = 0\\\frac{m}{2} - \frac{n}{3} - 8 = 0$$ m= n= $$\frac{p}{6} - 72 + \frac{q}{2} = 0\\\frac{p}{2} - \frac{q}{5} - 12 = 0$$ p= q= $$\frac{3r}{2} + \frac{s}{3} = 43 \\\frac{r}{4} + \frac{2s}{5} = 33$$ r= s= $$\frac{2u}{3} - 118 + \frac{5v}{2} = 0\\\frac{7u}{2} - \frac{v}{3} - 135 = 0$$ u= v= $$\frac{5w}{3} - 800 + \frac{5z}{4} = 0\\\frac{7w}{2} + \frac{z}{7} - 357 = 72$$ w= z=
Check

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

## 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.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

#### Hi-Low Predict

A version of the Play Your Cards Right TV programme. Calculate the probabilities of cards being higher or lower than the one shown. a fun way to practise applying probability and using fractions.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

Subscribe

## 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.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## 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:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All:

## Description of Levels

Close

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.

## 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!

## Example

###### 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.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you donâ€™t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Close