 # Using Graphs to Solve Equations

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

##### ExerciseExam-Style QuestionsRelated ResourcesHelp VideoMore Graphs
 1. Use the graphs to solve the simultaneous equationsy = 2x − 3 and y = 3 − 3x.Find the x value where the lines cross.  2. Use the graphs to solve the simultaneous equationsy = ½x − 2 and y = 1 − ½x.Find the x value where the lines cross.  3. Use the graphs to solve the simultaneous equationsy = ½x + 2 and y = x² − 2.Find the larger x value where the graphs cross. Give your answer to one decimal place.  4. Use the graphs to solve the simultaneous equationsy = 2 − ½x and y = x² − 2.Find the larger x value where the graphs cross. Give your answer to one decimal place.  5. Use the graphs to solve the simultaneous equationsy = x² − 1 and y = 1 − x².Find the smaller x value where the graphs cross. Give your answer to one decimal place.  6. Use the graphs to solve the simultaneous equationsy = x3 − 1 and y = 3 − x².Find the x value where the graphs cross. Give your answer to one decimal place.  7. Use the graphs to solve the simultaneous equationsy = x3 − 2 and y = ⅓x4 − x3 + x² − x.Find the x value where the graphs cross. Give your answer to one decimal place.  8. Use the graph to find the smaller solution of the equation:2x2 − 3x − 2 = 0.  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.  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.  Check

## 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.

Please contact me if you have any suggestions or questions. ## 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 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

#### River Crossing Three interactive versions of the traditional river crossing puzzles. The objective is to get all of the characters to the other side of the river without breaking any of the rules.

## 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.

Close ## 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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