Solving simultaneous equations by elimination from a context | Maths

Starter quiz

Which equation is true for $x = 4$ and $y = 5$ ?

$2x + y = 9$

$2x + 3y = 23$ ✓

$4x + y = 20$
If I add together the pair of simultaneous equations $9x + 3y = 10$ and $6x + y = 30$ , what is the resulting equation?

'15x + 4y = 40' ✓
Which equation is true for $x = 4$ and $y = 6$ ?

$3x + 2y = 24$ ✓

$3x + y = 20$

$x + 2y = 14$
If I add together the pair of simultaneous equations $3x + 2y = 10$ and $3y - 3x = 40$ , what is the resulting equation?

'5y = 50' ✓
Which equation is true for $x = -2$ and $y = 5$ ?

$3x + 2y = 6$

$3x + 2y = 4$ ✓

$3x + 2y = 11$
If I add together the pair of simultaneous equations $13x + 2y = 10$ and $7x - 2y = 40$ , what is the resulting equation?

'20x = 50' ✓

Exit quiz

If ◉ ◉ ◯ = 25 points and ◉ ◉ ◯ ◯ = 30 points, what is the value of ◉?

'10' ✓
If ◉ ◉ ◯ ◯ = 18 points and ◉ ◯ ◯ = 11 points, what is the value of ◉?

'7' ✓
If ◉ ◉ ◯ ◯ = 20 points and ◉ ◯ ◯ = 12 points, what is the value of ◯?

'2' ✓
If ◉ ◉ ◯ = 23 points and ◉ - (◯) = 10 points, what is the value of ◯?

'1' ✓
If ◉ ◉ ◯ = 17 points and ◉ - (◯) = 10 points, what is the value of ◯?

'-1' ✓
If ◉ ◉ ◉ ◯ = 33 points and ◉ ◉ ◉ ◯ ◯ = 36 points, what is the value of ◉?

'10' ✓

Worksheet

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Lesson Details

Key learning points

It is possible to find a solution that satisfies a problem with two unknowns by trial and error.
It is possible to use the difference between the two scenarios to create a third valid scenario.
Once you know one of the unknowns, you can substitute to find the other.

Common misconception

Subtracting the variables one way round but the constants the other way.

Pupils could rewrite their equations so the one they are subtracting is underneath in a column method. For this lesson, the answers are in context so pupils should spot when negative answers do not make sense.

Keywords

Simultaneous equations - Equations which represent different relationships between the same variables are called simultaneous equations.
Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.