A LevelMathsEdexcelPureExam QuestionsAlgebra & FunctionsSimultaneous Equations

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

Exam code: 9MA0

2 hours32 questions
Easy
Medium
Hard
1
2 marks

Solve

x plus y equals 8

x minus y equals 4

How did you do?

2
2 marks

Solve

2 x plus 5 y equals 3

6 x minus 10 y equals 34

How did you do?

3a
1 mark

Make y the subject of

4 x plus 2 y minus 6 equals 0

How did you do?

3b
2 marks

Use the result in part (a) to solve

4 x plus 2 y minus 6 equals 0

3 x plus 2 y minus 1 equals 1

How did you do?

4
3 marks

Solve

5 x minus 2 y minus 16 equals 0

3 x plus 7 y plus 15 equals 0

How did you do?

5
2 marks

Solve

y equals 2 x plus 3

4 x minus 3 y plus 4 equals negative 1

How did you do?

6
2 marks

Solve

7 x plus 4 y equals 17
3 x minus 2 y equals 11

How did you do?

7
3 marks

By making y the subject of x plus y equals negative 5, solve the simultaneous equations

2 x minus 5 y equals 4
x plus y equals negative 5

How did you do?

8
2 marks

Solve

3 x plus 4 y equals negative 13
2 x minus 3 y equals 14

How did you do?

9
2 marks

By making 2 y the subject of 3 x plus 2 y equals negative 12, solve

4 y minus 5 x equals negative 2
3 x plus 2 y equals negative 12

How did you do?

10
2 marks

Solve

6 x minus 15 y equals negative 1
9 x plus 20 y equals 7

How did you do?

11
2 marks

By making 2 x the subject of 5 y minus 2 x equals negative 1, solve

4 x plus 3 y equals 1
5 y minus 2 x equals negative 1

How did you do?

1
3 marks

Solve

y equals 2 x minus 1

x squared plus y squared minus 2 equals 0

How did you do?

2
3 marks

Solve

y equals x plus 3

2 x squared minus y squared equals 5 x plus 3

How did you do?

3a
2 marks

Given

3 x squared plus 4 y equals 83
3 x plus 2 y equals negative 11

show that

x squared minus 2 x minus 35 equals 0

How did you do?

3b
3 marks

Hence solve

3 x squared plus 4 y equals 83
3 x plus 2 y equals negative 11

How did you do?

4a
2 marks

Given

x squared plus 10 x plus y squared equals negative 20
y equals 2 x plus 10

show that

x squared plus 10 x plus 24 equals 0

How did you do?

4b
3 marks

Hence solve

x squared plus 10 x plus y squared equals negative 20
y equals 2 x plus 10

How did you do?

5a
2 marks

Given that

4 x minus k y equals 13
3 x plus 2 k y equals 7

where k is a constant, show that

x equals 3

How did you do?

5b
2 marks

Find an expression for y in terms of k.

How did you do?

5c
1 mark

Given that y equals 3, find k.

How did you do?

6
5 marks

Use algebra to solve

x plus 3 y minus 1 equals 0

x squared plus 9 y equals 2 minus y squared

How did you do?

7
4 marks

Solve

x plus y equals 4
x squared minus 4 x minus 3 y equals 0

How did you do?

8a
3 marks

Simultaneous equations in x and y are given by

3 k x plus y equals negative 4
2 k x minus 4 y equals 2

where k is a non-zero constant.

Solve the equations for x and space y, giving your answer in terms of k where necessary.

How did you do?

8b
1 mark

Find the value of k for which the x and y solutions are equal.

How did you do?

9
3 marks

Solve

4 x squared plus 2 x minus 6 y equals 4
2 x minus 3 y equals negative 1

How did you do?

1
3 marks

Use algebra to solve

y minus x minus 1 equals 0

left parenthesis 2 x plus 1 right parenthesis squared minus 3 y squared plus 3 x minus 10 equals 0

How did you do?

2a
2 marks

Simultaneous equations in x and y are given by

x squared minus 2 y equals 10
2 x minus y equals k

where k is a constant.

Show that

x squared minus 4 x plus 2 left parenthesis k minus 5 right parenthesis equals 0

How did you do?

2b
2 marks

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

How did you do?

2c
3 marks

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

How did you do?

3a
2 marks

Given

x squared minus 8 y equals negative 40
3 x plus 2 y equals 4

show that

x squared plus 12 x plus 24 equals 0

How did you do?

3b
Sme Calculator
3 marks

Hence solve

x squared minus 8 y equals negative 40
3 x plus 2 y equals 4

giving solutions for x and y in the form

a plus-or-minus b square root of 3

where a and b are integers to be found.

How did you do?

4a
2 marks

Given

4 x squared plus 5 x y plus 9 y squared equals 36
y equals 2 over 3 space x plus 2

show that 

x squared plus k x equals 0

where k is a constant to be found.

How did you do?

4b
2 marks

Hence solve

4 x squared plus 5 x y plus 9 y squared equals 36
y equals 2 over 3 space x plus 2

How did you do?

5a
2 marks

Given

15 x squared minus 4 y squared equals 12
4 x plus 2 y equals 1

show that

x squared minus 8 x plus 13 equals 0

How did you do?

5b
Sme Calculator
4 marks

Hence solve

15 x squared minus 4 y squared equals 12
4 x plus 2 y equals 1

giving solutions for x and y in the form

a plus-or-minus b square root of 3

where a and b are constants to be found.

How did you do?

6a
3 marks

Simultaneous equations in x and y are given by

x squared minus y plus 3 x equals k
20 x minus 4 y equals negative 5

where k is a constant.

The simultaneous equations have exactly one x solution and one y solution.

Find the value of k.

How did you do?

6b
3 marks

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

How did you do?

7
Sme Calculator
4 marks

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

How did you do?

8
Sme Calculator
4 marks

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

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

 h equals 0.84 x minus 0.07 x squared

The sloping roof of the shed can be modelled by

 h equals 2 plus 0.1 x

Graph with two lines: a linear line labelled "h = 2 + 0.1x" and a curved line labelled "h = 0.84x - 0.07x²." Axes labelled h and x.

According to the model, determine whether or not the firework hits the roof. Show your full working.

How did you do?

9
3 marks

Solve

9 x squared minus 7 x y plus 4 y squared equals 36
3 x plus 2 y equals negative 6

How did you do?

10a
2 marks

Given

8 y squared minus 3 x squared minus 4 x equals negative 11 over 2
3 x plus 4 y equals 1

 show that

3 x squared minus 14 x plus 12 equals 0

How did you do?

10b
Sme Calculator
3 marks

Hence solve

8 y squared minus 3 x squared minus 4 x equals negative 11 over 2
3 x plus 4 y equals 1

giving solutions for x and y in the form

a plus-or-minus b square root of c

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

How did you do?

11a
3 marks

Simultaneous equations in x and y are given by

5 x plus left parenthesis k plus 1 right parenthesis y equals negative 20
7 x minus 2 k y equals 2 y plus 6

where k is a constant.

Solve the equations for x and space y, giving your answers in terms of k where necessary.

How did you do?

11b
1 mark

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

How did you do?

12
5 marks

Simultaneous equations in x and y are given by

x squared plus 2 y squared equals 25
x minus y equals k

where k is a constant.

Find the possible values of k for which

(i) exactly one x solution exists

(ii) two distinct x solutions exist

(iii) no x solutions exist

How did you do?