# Using Graphs to Solve Equations

## 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

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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.

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## Help Video

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