Equations which represent different relationships between the same variables are called simultaneous equations.

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

Non-solutions to simultaneous linear equations

Maths

Checking and securing understanding of simultaneous equations

Inequalities on number lines

Solving simple linear inequalities

Solving more complicated linear inequalities

Linear inequalities in context

A single solution set

Solution set notation

Solving a linear inequality graphically

Solving a set of linear inequalities graphically

Relating graphical solutions to algebraic solutions for inequalities

Solving quadratic inequalities in one variable graphically

Solving quadratic inequalities algebraically

Advanced problem solving with linear inequalities

In this unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.

Inequalities

Which of these coordinates satisfy the inequality $$y>2x$$?

Using the graph of $$y=5-2x$$ (or otherwise) which coordinates satisfy the inequality $$y<5-2x$$? 

Solution to $$y=\frac{1}{2}x+3$$ but not a solution to $$y=3x-2$$

Solution to $$y=3x-2$$ but not a solution to $$y=\frac{1}{2}x+3$$

Solution to both $$y=3x-2$$ and $$y=\frac{1}{2}x+3$$ simultaneously

Not a solution to $$y=3x-2$$ nor a solution to $$y=\frac{1}{2}x+3$$

Match the solutions to the descriptions. Use the graphs to help you.

Which statements are true for the point (2, 3)?

Match the coordinates to the correct statements.

Which coordinate pair satisfies the inequalities $$y>x-1$$ and $$y<2x-1$$?

Match up the inequalities to the statements.

Which of these solutions satisfy the equation $$y=3x-1$$?

Which of these coordinates are on the line with equation $$y=2x+5$$?

Using the graph or otherwise, what is the solution to the equations $$y=2x+5$$ and $$y=2-x$$ simultaneously?

Which of these equations is $$x=5, y=3$$ a solution to? 

Starter Quiz

Match up the inequalities to the statements.