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

The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Checking and securing understanding of simultaneous equations

Maths

Non-solutions to simultaneous linear 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

The __________ shows us a value of $$x$$ and $$y$$ that satisfies two linear equations simultaneously when plotted.

Here are the lines with equations $$y=2x+1$$ and $$y=5-2x$$. What is the solution to both equations simultaneously?

How many solutions are there to the equations $$y=2x+8$$ and $$y=2x+3$$ when solved simultaneously?

How many solutions are there to the equations $$2y=3x+4$$ and $$4y-6x=8$$ when solved simultaneously?

Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$y=2x-4$$?

Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$3y+2x=12$$?

Which of these are solutions to the equation $$y=3x-4$$?

What is the gradient of the line with equation $$y=4x+2$$ ?

What is the gradient of the line with equation $$2y+5x=10$$ ?

What is the $$x$$ intercept of the line with equation $$3y+4x=12$$ ?

Fill in the missing coordinate for the $$y$$ intercept of the line with equation $$3y+4x=12$$ (0, {{}})

Which of these shows the line with equation $$2y=6-4x$$ ?

Starter Quiz

Which of these are solutions to the equation $$y=3x-4$$?