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Forming simultaneous equations

I can derive two different simultaneous equations from a context.

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Lesson 2 of 13

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Year 10

Forming simultaneous equations

I can derive two different simultaneous equations from a context.

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Lesson details

Key learning points

Relationships in context can be expressed using letters to represent the unknown values.
It is important to be clear about what each variable represents.
Two different statements can be connected via their variables.
One pair of values could satisfy more than one equation.

Keywords

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

Common misconception

Incorrectly identifying when simultaneous equations can be formed. This can lead to pupils using the same letter in two equations to represent different things.

Pupils should be writing down precisely what the variable represent in context. They can then compare whether they are using the same letter to represent the same thing in two different equations.

Pupils can use trial and error to find the solutions to the equations they form in task B. This should lead them to seeing a need for a more efficient method for solving equations simultaneously.

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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
If $$x = 11$$, what is the value of $$y$$ for $$6x + y = 70$$?

Correct Answer: 4, y= 4

Q2.
Which pair of coordinates does not sit on the line $$y = 5x + 2$$?

(1, 7)

(2, 12)

Correct answer: (-2, -12)

(0, 2)

Q3.
If $$x = -2$$, what is the value of $$y$$ for $$4x + 8y = 0$$?

Correct Answer: 1, y = 1

Q4.
If $$x = 2$$, what is the value of $$y$$ for $$10x + 2y = -8$$?

Correct Answer: -14, y -14

Q5.
Which pair of coordinates does not sit on the line $$y = x - 9$$?

Correct answer: (0, 9)

(2, -7)

(9, 0)

Q6.
Which point does not satisfy the equation $$3x^2 + 3x - 10 = y$$?

(-10, 260)

Correct answer: (9, 206)

(-8, 158)

Assessment exit quiz

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6 Questions

Q1.
The area of a rectangle is $$80 cm^2$$. The perimeter is $$48 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

Correct answer: $$ab = 80$$

$$a + b = 48$$

Correct answer: $$2(a + b) = 48$$

$$ab = 48$$

Q2.
Ryan (r) is 8 years older than his brother (b). A year ago, his brother was half the age Ryan will be next year.

$$r = 8$$

$$r = 8b$$

Correct answer: $$r - 1 = 2b$$

Correct answer: $$r = b + 8$$

Q3.
The area of a rectangle is $$18cm^2$$. The perimeter is $$22 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

$$ab = 22$$

$$a + b = 22$$

Correct answer: $$ab = 18$$

Correct answer: $$2a + 2b = 22$$

Q4.
Which two of the following are correct for a right triangle with sides $$a, b$$ and hypotenuse $$c$$?

$$a + b + c = abc$$

Correct answer: $$a^2 + b^2 = c^2$$

Correct answer: $$Perimeter = a + b + c$$

$$Perimeter = ab + c$$

Q5.
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?

$$a + b = 30$$

Correct answer: $$ab = 50$$

$$a = 4b$$

Q6.
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.

$$a + b = 4$$

Correct answer: $$a + b = 9$$

Correct answer: $$a = b - 4$$

$$a = b + 4$$

Lesson appears in

UnitMaths / Simultaneous equations: 2 variables

Maths

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Forming simultaneous equations

Forming simultaneous equations

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.If $$x = 11$$, what is the value of $$y$$ for $$6x + y = 70$$?

Q2.Which pair of coordinates does not sit on the line $$y = 5x + 2$$?

Q3.If $$x = -2$$, what is the value of $$y$$ for $$4x + 8y = 0$$?

Q4.If $$x = 2$$, what is the value of $$y$$ for $$10x + 2y = -8$$?

Q5.Which pair of coordinates does not sit on the line $$y = x - 9$$?

Q6.Which point does not satisfy the equation $$3x^2 + 3x - 10 = y$$?

Assessment exit quiz

6 Questions

Q1.The area of a rectangle is $$80 cm^2$$. The perimeter is $$48 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

Q2.Ryan (r) is 8 years older than his brother (b). A year ago, his brother was half the age Ryan will be next year.

Q3.The area of a rectangle is $$18cm^2$$. The perimeter is $$22 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

Q4.Which two of the following are correct for a right triangle with sides $$a, b$$ and hypotenuse $$c$$?

Q5.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?

Q6.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.

Lesson appears in

UnitMaths / Simultaneous equations: 2 variables

Maths

Q1.
If $$x = 11$$, what is the value of $$y$$ for $$6x + y = 70$$?

Q2.
Which pair of coordinates does not sit on the line $$y = 5x + 2$$?

Q3.
If $$x = -2$$, what is the value of $$y$$ for $$4x + 8y = 0$$?

Q4.
If $$x = 2$$, what is the value of $$y$$ for $$10x + 2y = -8$$?

Q5.
Which pair of coordinates does not sit on the line $$y = x - 9$$?

Q6.
Which point does not satisfy the equation $$3x^2 + 3x - 10 = y$$?

Q1.
The area of a rectangle is $$80 cm^2$$. The perimeter is $$48 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

Q2.
Ryan (r) is 8 years older than his brother (b). A year ago, his brother was half the age Ryan will be next year.

Q3.
The area of a rectangle is $$18cm^2$$. The perimeter is $$22 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$?

Q4.
Which two of the following are correct for a right triangle with sides $$a, b$$ and hypotenuse $$c$$?

Q5.
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?

Q6.
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.