WJEC GCSE Maths
Topic questions Pure mathematics Simultaneous equations
30 questions · 133 marks · about 3 hours
Use an algebraic method, not trial and improvement, to find the total cost of 
kg of cherries and 6 kg of grapes.
You must show all your working.
The total cost of 
kg of cherries and 6 kg of grapes is £…………........ ……………
2400 tickets were sold for a concert. The table below shows the cost of the different types of ticket.
| Ticket | Cost per ticket |
| SEATED | £45 |
| STANDING | £23 |
The total cost of all the 2400 tickets sold was £89 520. Let x represent the number of seated tickets sold. Let y represent the number of standing tickets sold.
Complete the following table.
2400 tickets were sold for a concert. The table below shows the cost of the different types of ticket.
| Ticket | Cost per ticket |
| SEATED | £45 |
| STANDING | £23 |
The total cost of all the 2400 tickets sold was £89 520. Let x represent the number of seated tickets sold. Let y represent the number of standing tickets sold.
Complete the following table.
A kite and an isosceles triangle are shown below.
They are not drawn to the same scale.
Using the information shown on the kite, calculate the perimeter of the isosceles triangle. Do not use a trial and improvement method.
You must show all your working.
A kite and an isosceles triangle are shown below.
They are not drawn to the same scale.
Using the information shown on the kite, calculate the perimeter of the isosceles triangle. Do not use a trial and improvement method.
You must show all your working.
Andrew and Grace each have some £10 notes and £5 notes. Andrew has 6 notes. The total value of Andrew’s notes is £55. Grace has 5 notes. The total value of Grace’s notes is £35.
How many £10 notes do they have in total?
How many £5 notes do they have in total?
Solve the following simultaneous equations using an algebraic (not graphical) method.
You must show all your working.
Solve the following simultaneous equations using an algebraic (not graphical) method.
You must show all your working.
The diagram below shows an isosceles triangle and a square.
Perimeter of triangle = 19 cm
Diagram not drawn to scale
Use an algebraic method (not trial and improvement) to find the value of x and the value of y
You must show all your working.
The diagram below shows an isosceles triangle and a square.
Perimeter of triangle = 19 cm
Diagram not drawn to scale
Use an algebraic method (not trial and improvement) to find the value of x and the value of y.
You must show all your working.
The Morgan family and the Smith family are on holiday in Aberystwyth.
There are 7 adults and 2 children in the Morgan family. There are 4 adults and 3 children in the Smith family.
Both families visit a Craft Centre. The entry price to the Craft Centre is £x for adults and £y for children.
The total cost for the Morgan family is £41.50. The total cost for the Smith family is £29.75.
Form two equations in terms of x and y.
Solve your equations, using an algebraic method, to find the entry price for adults and the entry
price for children.
The Morgan family and the Smith family are on holiday in Aberystwyth.
There are 7 adults and 2 children in the Morgan family. There are 4 adults and 3 children in the Smith family.
Both families visit a Craft Centre. The entry price to the Craft Centre is £x for adults and £y for children.
The total cost for the Morgan family is £41.50. The total cost for the Smith family is £29.75.
Form two equations in terms of x and y.
Solve your equations, using an algebraic method, to find the entry price for adults and the entry
price for children.
What is the gradient of the straight line with equation 6 y = 3 x + 7 ?
Circle the correct answer.
What is the value of y at the point where the line 5x + y + 3 = 0 crosses the y-axis?
Circle the correct answer.
What are the coordinates of the point where the lines with equations x + y = 7 and x − y = 3 intersect?
Circle the correct answer.
(4, 3)
(7, 4)
(5, 2)
(3, 7)
(−5, 2)
What is the gradient of the straight line with equation 6 y = 3 x + 7 ?
Circle the correct answer.
What is the value of y at the point where the line 5x + y + 3 = 0 crosses the y-axis?
Circle the correct answer.
What are the coordinates of the point where the lines with equations x + y = 7 and x − y = 3 intersect?
Circle the correct answer.
(4, 3)
(7, 4)
(5, 2)
(3, 7)
(−5, 2)
A rectangle of length 12 cm and width (2x – y)cm has an area of 72 cm2.
KLMN is a kite where KL = 3xcm and LM = ycm.
The perimeter of the kite KLMN = 33 cm.
Calculate the values of x and y.
You must show all your working.
Do not use a trial and improvement method.
Also involves Area and perimeter
A rectangle of length 12 cm and width (2x – y)cm has an area of 72 cm2.
KLMN is a kite where KL = 3xcm and LM = ycm.
The perimeter of the kite KLMN = 33 cm.
Calculate the values of x and y.
You must show all your working.
Do not use a trial and improvement method.
Memes
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