Solving simultaneous equations via any method | Maths

Starter quiz

Using substitution, what is the value of $x$ for simultaneous equations $6x + 4y = 32$ and $3x + 9y = 51$ ?

'2' ✓
Using substitution, what is the value of $x$ for simultaneous equations $7x + 2y = 36$ and $4x + 2y = 30$ ?

'2' ✓
Using substitution, what is the value of $y$ for simultaneous equations $y - x = -1$ and $3x + y = 19$ ?

'4' ✓
Which multiplier would match the x coefficients for equations 1) $6x + 10y = 42$ and 2) $x + 2y = 8$ :

multiply equation 1) by 2

multiply equation 1) by 3

multiply equation 2) by 6 ✓

multiply equation 2) by 5
What is the value of $y$ for simultaneous equations $x + 4y = 7$ and $2x + 3y = -1$

'3' ✓
What is the value of $x$ for simultaneous equations $x + y = 7$ and $6x + 3y = 27$

'2' ✓

Exit quiz

Solve using any method: $3x + 5y = -6$ and $5x - 5y = 30$ . Write your answer in the form $(x,y)$ .

'(3, -3)' ✓
Solve using any method: $3x + y = 15$ and $5x - 5y = 45$ . Write your answer in the form $(x,y$ ).

'(6, -3)' ✓
Solve using any method: $6x + 2y = 30$ and $6x - 5y = 51$ . Write your answer in the form $(x,y)$ .

'(6, -3)' ✓
Solve using any method: $8x + 2y =10$ and $3x - 4y = 18$ . Write your answer in the form $(x,y)$ .

'(2, -3)' ✓
Solve using any method: $x + 5y =24$ and $5x + 3y = 10$ . Write your answer in the form $(x,y)$ .

'(-1, 5)' ✓
Solve using any method: $5x + 4y = 11$ and $2x + 5y = 35$ . Write your answer in the form $(x,y)$ .

'(-5, 9)' ✓

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Lesson Details

Key learning points

The features of the equations may mean one method is more preferable for solving.
You can use any of the methods that are valid.
You can use the other methods to check your solution.
The solution should be interpreted in context if context was stated.

Common misconception

One method is superior when solving simultaneous equations.

Understanding that there are often multiple ways to solve the same problem and then be able to accurately execute a variety of methods is very useful. In this topic, it can enable pupils to confirm their solutions.

Keywords

Substitution - Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.
Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.