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

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.

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? 

This lesson will be removed by end of Summer Term 2025.

Non-solutions to simultaneous linear equations

Lesson outcome

This lesson will be removed by end of Summer Term 2025.