Transum Software

Using Graphs to Solve Equations

Use the graphs provided to solve both simultaneous and quadratic equations.

Exercise Exam-Style Questions Related Resources Help Video More Graphs
1. Use the graphs to solve the simultaneous equations
y = 2x − 1 and y = 2 − 3x.
Find the x value where the lines cross.


Correct Wrong

2. Use the graphs to solve the simultaneous equations
y = ½x − 3 and y = 2 − ½x.
Find the x value where the lines cross.


Correct Wrong

3. Use the graphs to solve the simultaneous equations
y = ½x + 1 and y = x² − 2.
Find the larger x value where the graphs cross. Give your answer to one decimal place.


Correct Wrong

4. Use the graphs to solve the simultaneous equations
y = 2 − ½x and y = x² − 2.
Find the larger x value where the graphs cross. Give your answer to one decimal place.


Correct Wrong

5. Use the graphs to solve the simultaneous equations
y = x² − 2 and y = 2 − x².
Find the smaller x value where the graphs cross. Give your answer to one decimal place.


Correct Wrong

6. Use the graphs to solve the simultaneous equations
y = x3 − 1 and y = 3 − x².
Find the x value where the graphs cross. Give your answer to one decimal place.


Correct Wrong

7. Use the graphs to solve the simultaneous equations
y = x3 − 2 and y = ⅓x4 − x3 + x² − x.
Find the x value where the graphs cross. Give your answer to one decimal place.


Correct Wrong

8. Use the graph to find the smaller solution of the equation:
2x2 − 3x − 2 = 0.


Correct Wrong

9. Use the graph of:
y = 2x2 − 3x − 2.
to find the largest solution of 2x2 − 3x − 5 = 0. Give your answer to one decimal place.


Correct Wrong

10. Use the graph of:
y = 2x2 − 3x − 2.
to find the largest solution of 2x2 − 3x − 1 = 0. Give your answer to one decimal place.


Correct Wrong

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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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Featured Activity

Hi-Low Predict

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.

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.

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:

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Related Resources

Simultaneous Equations - A series of exercises in increasing order of difficulty on solving simultaneous equations algebraically.

Plotting Graphs - Complete a table of values then plot the corresponding points to create a graph.

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

More on this topic including lesson Starters, visual aids and investigations.

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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Example

This video is from the excellent HegartyMaths.

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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