Forming simultaneous equations from a context Revision Card

AI generatedAlgebraKS3 / GCSE

Forming simultaneous equations from a context.

The same pair of values must satisfy both equations.
For elimination, multiply every term of an equation by the same number. For substitution, replace a variable by an equal expression.
Substitute the final pair into both original equations to check.

Example 1

1 notebooks and 2 pens cost £3. 2 notebooks and 3 pens cost £5. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 6.

Multiply every term of (1) by 3.

Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).

Example 2

2 notebooks and 3 pens cost £7. 3 notebooks and 4 pens cost £10. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 12.

Multiply every term of (1) by 4.

Multiply every term of (2) by 3. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).

Your turn

Question 1

3 notebooks and 4 pens cost £13. 4 notebooks and 5 pens cost £17. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Check answer

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 20.

Multiply every term of (1) by 5.

Multiply every term of (2) by 4. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).

Question 2

4 notebooks and 2 pens cost £18. 5 notebooks and 3 pens cost £23. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Check answer

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 6.

Multiply every term of (1) by 3.

Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).

Question 3

1 notebooks and 3 pens cost £8. 2 notebooks and 4 pens cost £14. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Check answer

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 12.

Multiply every term of (1) by 4.

Multiply every term of (2) by 3. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).

Question 4

2 notebooks and 4 pens cost £16. 3 notebooks and 5 pens cost £23. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Check answer

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 20.

Multiply every term of (1) by 5.

Multiply every term of (2) by 4. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).

Question 5

3 notebooks and 2 pens cost £23. 4 notebooks and 3 pens cost £31. Find the price of one notebook and one pen. Let be the notebook price and be the pen price, in pounds.

Check answer

Label this equation (1).

Label this equation (2). Match the coefficients of

using their lowest common multiple, 6.

Multiply every term of (1) by 3.

Multiply every term of (2) by 2. Subtract the new second equation from the new first equation to eliminate

Substitute

into (1).