New
New
Year 11
Higher

Solving a set of linear inequalities graphically

I can extend my thinking to multiple linear inequalities with 2 variables and can show this can be solved graphically to find a solution set.

New
New
Year 11
Higher

Solving a set of linear inequalities graphically

I can extend my thinking to multiple linear inequalities with 2 variables and can show this can be solved graphically to find a solution set.

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Lesson details

Key learning points

  1. Multiple linear inequalities in two variables can be graphed on the same axes
  2. By testing points in the various equations, you can determine the region that satisfies all the inequalities
  3. This region is the solution set

Keywords

  • Inequality - An inequality is used to show that one expression may not be equal to another.

  • Region - A region is an area that graphically represents the solutions to one or more inequalities. Every coordinate pair within the region satisfies the inequalities that define the region.

Common misconception

All inequalities are graphed with solid lines.

When graphed, strict inequalities are indicated with a dashed line. This is important as it visually tells us that values on the line will not satisfy the inequality.

Encourage pupils to identify the region that satisfies multiple inequalities in different ways: graphically, testing a point, algebraically.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
A region is an area that can graphically represent the solutions to one or more...
expressions.
equations.
Correct answer: inequalities.
Q2.
Which values satisfy this inequality? $$x\le-7$$
Correct answer: $$-7$$
$$-6$$
Correct answer: $$-7.5$$
Correct answer: $$-12\;784$$
$$8$$
Q3.
Which inequality is represented by this region?
An image in a quiz
$$x>3$$
$$x<3$$
Correct answer: $$y>3$$
$$y<3$$
$$y\geq3$$
Q4.
Which of these coordinate pairs is in the region satisfied by $$y\geq-x$$?
Correct answer: $$(0,0)$$
Correct answer: $$(8,8)$$
$$(-8,-8)$$
Correct answer: $$(8,-4)$$
$$(-8,4)$$
Q5.
Which inequality is represented by this region?
An image in a quiz
$$y\le5-2x$$
$$y\geq5-2x$$
$$y<2x-5$$
$$y>2x-5$$
Correct answer: $$y\geq2x-5$$
Q6.
Which of these coordinate pairs is in the region satisfied by $$y<4x+5$$?
Correct answer: $$(0,0)$$
Correct answer: $$(2,2)$$
Correct answer: $$(2,-2)$$
$$(-2,2)$$
$$(-2,-2)$$

6 Questions

Q1.
This region satisfies both inequalities $$x>-5$$ and $$y<3$$...
An image in a quiz
Correct answer: simultaneously.
separately.
singularly.
Q2.
Which region satisfies both inequalities simultaneously? $$y<-x$$ and $$x>-5$$
An image in a quiz
R1
Correct answer: R2
R3
R4
Q3.
Which coordinate pairs satisfy both of these inequalities simultaneously? $$y<x$$ and $$y>2$$
$$(4,4)$$
$$(4,5)$$
Correct answer: $$(5,4)$$
Correct answer: $$(4,3)$$
$$(3,4)$$
Q4.
In which region are all three of these inequalities satisfied simultaneously? $$y<4$$, $$y>x-3$$ and $$y>-x-2$$
An image in a quiz
R1
R2
R3
R4
Correct answer: R5
Q5.
In which region are all three of these inequalities satisfied simultaneously? $$y<4$$, $$y<x-3$$ and $$y>-x-2$$
An image in a quiz
R1
Correct answer: R2
R3
R4
R5
Q6.
In which region are all three of these inequalities satisfied simultaneously? $$y>4$$, $$y<x-3$$ and $$y<-x-2$$
An image in a quiz
R1
R2
R3
R4
Correct answer: No region can satisfy all three simultaneously