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

Forming simultaneous equations

Maths

In the future 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 the prior unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in this unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

Simultaneous equations: 2 variables

The area of a rectangle is $$80 cm^2$$. The perimeter is $$48 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$? 

Ryan (r) is 8 years older than his brother (b). A year ago, his brother was half the age Ryan will be next year.

The area of a rectangle is $$18cm^2$$. The perimeter is $$22 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

Which two of the following are correct for a right triangle with sides $$a, b$$ and hypotenuse $$c$$? 

For a rectangle, the perimeter of a rectangle with side lengths $$a$$ and $$b$$ is 30 cm. The length is double the width. Which statement is true?


There are 9 goals scored in a football match. Team A scored $$a$$ goals, and winning Team B scored $$b$$ goals. The winning team scored 4 more than the losing team.

If $$x = 11$$, what is the value of $$y$$ for  $$6x + y = 70$$? 

Which pair of coordinates does not sit on the line $$y = 5x + 2$$?

If $$x = -2$$, what is the value of $$y$$ for  $$4x + 8y = 0$$? 

If $$x = 2$$, what is the value of $$y$$ for  $$10x + 2y = -8$$? 

Which pair of coordinates does not sit on the line $$y = x - 9$$?

Which point does not satisfy the equation $$3x^2 + 3x - 10 = y$$?

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

Forming simultaneous equations

Lesson outcome

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