Forming simultaneous equations | Maths | Quizalize & Oak National Academy

Starter quiz

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

'4' ✓
Which pair of coordinates does not sit on the line $y = 5x + 2$ ?

(1, 7)

(2, 12)

(-2, -12) ✓

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

'1' ✓
If $x = 2$ , what is the value of $y$ for $10x + 2y = -8$ ?

'-14' ✓
Which pair of coordinates does not sit on the line $y = x - 9$ ?

(0, 9) ✓

(2, -7)

(9, 0)
Which point does not satisfy the equation $3x^2 + 3x - 10 = y$ ?

(-10, 260)

(9, 206) ✓

(-8, 158)

Exit quiz

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

$ab = 80$ ✓

$a + b = 48$

$2(a + b) = 48$ ✓

$ab = 48$
Ryan (r) is 8 years older than his brother (b). A year ago, his brother was half the age Ryan will be next year.

$r = 8$

$r = 8b$

$r - 1 = 2b$ ✓

$r = b + 8$ ✓
The area of a rectangle is $18cm^2$ . The perimeter is $22 cm$ . Which two equations are true for side lengths $a$ and $b$ ?

$ab = 22$

$a + b = 22$

$ab = 18$ ✓

$2a + 2b = 22$ ✓
Which two of the following are correct for a right triangle with sides $a, b$ and hypotenuse $c$ ?

$a + b + c = abc$

$a^2 + b^2 = c^2$ ✓

$Perimeter = a + b + c$ ✓

$Perimeter = ab + c$
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?

$a + b = 30$

$ab = 50$ ✓

$a = 4b$
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.

$a + b = 4$

$a + b = 9$ ✓

$a = b - 4$ ✓

$a = b + 4$

Worksheet

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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.

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.

Keywords

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