# Using Graphs to Solve Equations

## Using and creating graphs to solve quadratics and pairs of simultaneous equations.

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 A Graphic Display Calculator is require for this level. If you don't have a GDC try this Graph Plotter. Use your GDC to find a solution to the following simultaneous equations:$$\quad \quad y=2.9x-40$$$$\quad \quad y=23-1.1x$$Give your answers correct to three significant figures. $$x =$$ ☐ ✓ ✗ ☐$$y =$$ ☐ ✓ ✗ 3 Solve the following simultaneous equations when $$0 \lt x \lt 10$$:$$\quad \quad y=\log{x}$$$$\quad \quad y=\frac{5}{x-7}+3$$Give the y value correct to three significant figures. ☐$$y =$$ ☐ ✓ ✗ 4 Solve the following simultaneous equations where $$x$$ is measured in degrees:$$\quad \quad y=2\sin{(x+25)}$$$$\quad \quad y=3x$$Give the x value correct to three significant figures. ☐$$x =$$ ☐ ✓ ✗ 5 Solve the following simultaneous equations where $$x$$ is measured in radians:$$\quad \quad y=2\sin{(x+25)}$$$$\quad \quad y=3x$$Give the x value correct to three significant figures. ☐$$x =$$ ☐ ✓ ✗ 6 Solve the following simultaneous equations where $$x$$ is measured in degrees:$$\quad \quad y=3^x-10$$$$\quad \quad xy=\cos{x}$$Give the y value of the solution that has a positive x value correct to three significant figures. ☐$$y =$$ ☐ ✓ ✗
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This is Using Graphs to Solve Equations level 4. You can also try:
Level 1 Level 2 Level 3

## 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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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?

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Could we have some on angles too please?"

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#### Lemon Law

A fascinating digit changing challenge. Change the numbers on the apples so that the number on the lemon is the given total. Can you figure out, by understanding place value, how this works?

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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

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## Description of Levels

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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.

## Help Video

Instructions for using the TI-Nspire GDC can be found here.

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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