Solving a set of linear inequalities graphically | Maths

Starter quiz

A region is an area that can graphically represent the solutions to one or more...

expressions.

equations.

inequalities. ✓
Which values satisfy this inequality? $x\le-7$

$-7$ ✓

$-6$

$-7.5$ ✓

$-12\;784$ ✓

$8$
Which inequality is represented by this region?

$x>3$

$x<3$

$y>3$ ✓

$y<3$

$y\geq3$
Which of these coordinate pairs is in the region satisfied by $y\geq-x$ ?

$(0,0)$ ✓

$(8,8)$ ✓

$(-8,-8)$

$(8,-4)$ ✓

$(-8,4)$
Which inequality is represented by this region?

$y\le5-2x$

$y\geq5-2x$

$y<2x-5$

$y>2x-5$

$y\geq2x-5$ ✓
Which of these coordinate pairs is in the region satisfied by $y<4x+5$ ?

$(0,0)$ ✓

$(2,2)$ ✓

$(2,-2)$ ✓

$(-2,2)$

$(-2,-2)$

Exit quiz

This region satisfies both inequalities $x>-5$ and $y<3$ ...

simultaneously. ✓

separately.

singularly.
Which region satisfies both inequalities simultaneously? $y<-x$ and $x>-5$

R1

R2 ✓

R3

R4
Which coordinate pairs satisfy both of these inequalities simultaneously? $y and y>2$

$(4,4)$

$(4,5)$

$(5,4)$ ✓

$(4,3)$ ✓

$(3,4)$
In which region are all three of these inequalities satisfied simultaneously? $y<4$ , $y>x-3$ and $y>-x-2$

R1

R2

R3

R4

R5 ✓
In which region are all three of these inequalities satisfied simultaneously? $y<4$ , $y and y>-x-2$

R1

R2 ✓

R3

R4

R5
In which region are all three of these inequalities satisfied simultaneously? $y>4$ , $y and y<-x-2$

R1

R2

R3

R4

No region can satisfy all three simultaneously ✓

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

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

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.

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.