Transum Software

Using Graphs to Solve Equations

Using and creating graphs to solve quadratics and pairs of simultaneous equations.
  Menu   Level 1 Level 2 Level 3 Level 4 Exam-style   Help     More  

Equations:

\(2y = x + 5\)

\(2y+x+5=0\)

\(y=(x+1)^2\)

\(y=x^3 -11x^2 +39x -45\)

\(y=-x^3 -11x^2 -39x -49\)

\(x^2 + y^2 = 25\)

There are six equations shown to the left and their graphs are shown above. Your first job is to work out which equation describes which graph.

Use the graphs to find a solution to the following simultaneous equations:

\( \quad \quad 2y = x + 5\)
\( \quad \quad 2y + x + 5 = 0\)

\(x =\) ☐ ✓ ✗ ☐\(y =\) ☐ ✓ ✗

3

Use the graphs to find a positive value of \(x\) which satisfies the simultaneous equations:

\( \quad \quad 2y = x + 5\)
\( \quad \quad x^2 + y^2 = 25\)

☐\(x =\) ☐ ✓ ✗

4

Use the graphs to find a negative value of \(y\) which satisfies the simultaneous equations:

\( \quad \quad 2y + x + 5 = 0\)
\( \quad \quad x^2 + y^2 = 25\)

☐\(y =\) ☐ ✓ ✗

5

Use the graphs to find a negative value of \(x\) which satisfies the simultaneous equations:

\( \quad \quad y = (x + 1)^2\)
\( \quad \quad x^2 + y^2 = 25\)

☐\(x =\) ☐ ✓ ✗

6

Use the graphs to find an integer (whole number) value of \(x\) which satisfies the simultaneous equations:

\( \quad \quad y = x^3 -11x^2 +39x -45\)
\( \quad \quad x^2 + y^2 = 25\)

☐\(x =\) ☐ ✓ ✗

7

Find the value of \(x\) which satisfies the simultaneous equations:

\( \quad \quad y = -7\)
\( \quad \quad y=-x^3 -11x^2 -39x -49\)

☐\(x =\) ☐ ✓ ✗

8

Find the value of \(y\) which satisfies the simultaneous equations:

\( \quad \quad x = 2\)
\( \quad \quad y = x^3 -11x^2 +39x -45\)

☐\(y =\) ☐ ✓ ✗

9

Use the graphs to find a value of the largest solution of the equation:

\( \quad \quad (x + 1)^2 - 3 = 1\)

☐\(x =\) ☐ ✓ ✗

10

Use the graphs to find a value, to one decimal place, of the smallest solution of the equation:

\( \quad \quad (x + 1)^2 - \frac{x}{2} - \frac{5}{2} = 0\)

☐\(x =\) ☐ ✓ ✗

Check

This is Using Graphs to Solve Equations level 2. You can also try:
Level 1 Level 3 Level 4

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.
Recently Updated

Factorising

Factorising

Practise the skills of algebraic factorisation in this structured online self-marking exercise. So far this activity has been accessed 53851 times and 34070 Transum Trophies have been awarded for completing it.
Why am I learning this?

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 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity

Online Logo

Online Logo

An opportunity for students to write a computer program. There is nothing to download, all of the interaction takes place in the browser. Great for understanding angles and the properties of shapes.

Answers

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.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

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:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

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 Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program
©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://www.Transum.org/go/?Num=373

Description of Levels

Close

❎

Level 1 - The original basic exercise

Level 2 - A collection of graphs already drawn with related questions

Level 3 - Graphs to draw with pencil and paper in order to find solitions

Level 4 - For older students who have access to a Graphic Display Calculator (GDC).

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 Graphs including lesson Starters, visual aids, investigations and self-marking exercises.

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

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.

Log in Sign up

Help Video

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.

Log in Sign up

Close

❎