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

Forming simultaneous equations

Maths

Checking and securing understanding of interpreting graphs

Combining equations

Solving simultaneous equations by elimination from a context

Solving algebraic simultaneous equations by elimination

Solving more complex simultaneous equations by elimination

Solving simultaneous linear equations by substitution

Solving simultaneous linear equations graphically

Solving a quadratic and linear pair of simultaneous equations using elimination

Solving a quadratic and linear pair of simultaneous equations using substitution

Solving a quadratic and linear pair of simultaneous equations graphically

Solving simultaneous equations via any method

Problem solving with linear and quadratic simultaneous equations

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.

In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.

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 $$3x^2 + 3x - 10 = y$$?

Forming simultaneous equations

Lesson outcome