Simultaneous Equations (Edexcel A Level Maths: Pure): Exam Questions

Solve

Solve

Given

show that

Hence solve

Given

show that

Hence solve

Given that

where  is a constant, show that

Find an expression for in terms of .

Given that , find .

Use algebra to solve

Solve

Simultaneous equations in and are given by

where  is a non-zero constant.

Solve the equations for  and , giving your answer in terms of where necessary.

Find the value of for which the  and  solutions are equal.

Solve

Use algebra to solve

Simultaneous equations in and are given by

where  is a constant.

Show that

Find the value of for which the simultaneous equations have only one solution and one solution.

Using the value of in part (b), solve the simultaneous equations.

Given

show that

Hence solve

giving solutions for and in the form

where and are integers to be found.

Given

show that 

where is a constant to be found.

Hence solve

Given

show that

Hence solve

giving solutions for and in the form

where and are constants to be found.

Simultaneous equations in and are given by

where  is a constant.

The simultaneous equations have exactly one solution and one solution.

Find the value of .

Using the value of in part (a), solve the simultaneous equations.

You are asked to advise a client on which parcel delivery service to use to deliver parcels of differing sizes. 

• Linear Deliveries charge a flat rate of £2.25 per parcel, plus 40p times the mass of the parcel in kilograms

• Square Deal Deliveries charge a flat rate of £4 per parcel, plus 1p times the square of the parcel’s mass in kilograms

Form and solve simultaneous equations to find the two weights of parcels that are the same price in both companies.

Hence, find

• the range of weights of parcels for which Linear Deliveries is cheaper

• the range of weights of parcels for which Square Deal Deliveries is cheaper

A firework is launched inside a large shed with a sloping roof. 

The horizontal distance from the point it was launched, metres, and the height of the firework, metres, can be modelled by

The sloping roof of the shed can be modelled by

According to the model, determine whether or not the firework hits the roof.

Solve

Given

 show that

Hence solve

giving solutions for and in the form

where and are rational numbers to be found and is a prime number to be found.

Simultaneous equations in and are given by

where  is a constant.

Solve the equations for  and , giving your answers in terms of where necessary.

Find the value of  for which there are no solutions to the simultaneous equations.

Simultaneous equations in and are given by

where  is a constant.

Find the possible values of for which

(i) exactly one solution exists

(ii) two distinct solutions exist

(iii) no solutions exist