Browse Simultaneous equations

50 questions at your level

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

Simultaneous equations by elimination

19 questions

LessonNot started

Solve the simultaneous equations

\quad x + y = 10 \quad

\quad x - y = 4

●●●●●Level 12 marksStart

Solve the simultaneous equations

\quad 2x + y = 11 \quad

\quad x + y = 7

●●●●●Level 12 marksStart

Solve the simultaneous equations

2x + y = 11

x + y = 7

●●●●●Level 23 marksStart

Solve the simultaneous equations

2x + 3y = 12

2x - y = 4

●●●●●Level 23 marksStart

Solve the simultaneous equations

3x + 2y = 19

x - 2y = 1

●●●●●Level 23 marksStart

Solve the simultaneous equations

5x + 3y = 21

2x + 3y = 12

●●●●●Level 23 marksStart

Use these graphs to solve the simultaneous equations

x + 2y = 8

y = 2x - 6

●●●●●Level 21 markStart

Solve the simultaneous equations

3x + 2y = 19

x - 2y = 1

●●●●●Level 33 marksStart

Solve the simultaneous equations

4x + 3y = 10

2x + y = 4

●●●●●Level 33 marksStart

Solve the simultaneous equations

3x + 4y = 24

5x - 4y = 8

●●●●●Level 33 marksStart

Solve the simultaneous equations

4x + 3y = 24

2x - y = 2

●●●●●Level 33 marksStart

Solve the simultaneous equations

5x + 2y = 11

3x - 4y = 4

●●●●●Level 33 marksStart

3

2

3.55

5

4

6.35

Work out the cost of one pen and the cost of one ruler. Give your answers in pence. (3 marks)

●●●●●Level 33 marksStart

Solve the simultaneous equations

5x + 2y = 11

3x + 5y = 18

●●●●●Level 44 marksStart

Solve the simultaneous equations

2x - 3y = 13

3x + 2y = 13

●●●●●Level 44 marksStart

A cinema sells adult tickets and child tickets.

3 adult tickets and 2 child tickets cost £24.30.

2 adult tickets and 3 child tickets cost £21.20.

Work out the cost of one adult ticket and the cost of one child ticket.

●●●●●Level 44 marksStart

Solve the simultaneous equations

2x + 5y = 24

x + 2y = 10

●●●●●Level 43 marksStart

Solve the simultaneous equations

3x + 2y = 12

5x + 3y = 19

●●●●●Level 43 marksStart

5

2

3.40

.

3

4

4.00

.

Work out the cost of one pen and the cost of one ruler.

●●●●●Level 54 marksStart

Substitution and real-world simultaneous equations

18 questions

LessonNot started

y = 2x

x + y = 12

x

y

●●●●●Level 12 marksStart

y = x + 3

x + y = 11

. Find the value of

y

●●●●●Level 12 marksStart

3x + y = 14

y = 2

x

●●●●●Level 11 markStart

Two apples and one banana cost

80

p. One apple and one banana cost

50

p. Find the cost of one apple.

●●●●●Level 22 marksStart

Solve the simultaneous equations

y = 2x - 3

x + y = 9

●●●●●Level 33 marksStart

Solve the simultaneous equations

y = x + 4

3x + y = 16

●●●●●Level 33 marksStart

Solve the simultaneous equations

y = 2x - 3

3x + 2y = 15

●●●●●Level 33 marksStart

3

2

3.55

5

4

6.35

Work out the cost of one pen and the cost of one ruler. Give your answers in pence. (3 marks)

●●●●●Level 33 marksStart

3

2

10.10

2

5

12.05

Work out the cost of one coffee and the cost of one tea. [4]

●●●●●Level 34 marksStart

Solve the simultaneous equations

y = 3x + 1

2x + 3y = 25

●●●●●Level 43 marksStart

Two numbers have a sum of 41 and a difference of 9.

Find the two numbers.

●●●●●Level 43 marksStart

The length of a rectangle is 3 cm more than twice its width.

The perimeter of the rectangle is 24 cm.

(a) Find the length and the width of the rectangle.

(b) Work out the area of the rectangle.

●●●●●Level 44 marksStart

Solve the simultaneous equations

y = 2x + 1

5x - 2y = 8

●●●●●Level 43 marksStart

Two numbers have a sum of

52

.

One number is three times the other.

Find the two numbers.

●●●●●Level 43 marksStart

A burger costs £

1.50

more than a portion of fries.

2

3

portions of fries cost £

13

.

Work out the cost of one burger.

●●●●●Level 43 marksStart

6

m of green ribbon and

4

m of gold ribbon cost a total of

680

1

m of green ribbon : cost of

1

m of gold ribbon

= 3 : 4

Work out the cost of

1

m of green ribbon and the cost of

1

m of gold ribbon.

(4 marks)

●●●●●Level 44 marksStart

y = 3x - 5

y = x + 7

cross at the point

P

.

Work out the coordinates of

P

●●●●●Level 53 marksStart

y = 2x - 1

y = 7 - 2x

cross at the point

P

.

Work out the coordinates of

P

●●●●●Level 53 marksStart

Simultaneous equations — one linear, one quadratic

14 questions

LessonNot started

Solve the simultaneous equations

y = x^2 - 3x + 4

y = x + 1

●●●●●Level 44 marksStart

Solve the simultaneous equations

y = x^2

y = 2x + 8

●●●●●Level 44 marksStart

Solve the simultaneous equations

y = x^2 - 2x

y = x + 4

●●●●●Level 44 marksStart

Solve the simultaneous equations

y = x^2 + 3x - 5

y = 2x + 1

●●●●●Level 44 marksStart

Solve the simultaneous equations

x^2 + y^2 = 25

y = x + 1

●●●●●Level 45 marksStart

Solve the simultaneous equations

y = x^2 - 2

y = x + 4

●●●●●Level 45 marksStart

Solve the simultaneous equations

x^2 + y^2 = 34

y = x + 2

●●●●●Level 45 marksStart

Solve the simultaneous equations

x^2 + y^2 = 25

y = x + 1

Give your answers as coordinate pairs.

●●●●●Level 55 marksStart

y = x - 3

meets the circle

x^2 + y^2 = 17

A

B

.

(a) Show that

2x^2 - 6x - 8 = 0

A

B

.

(b) Find the coordinates of

A

B

●●●●●Level 55 marksStart

Show that the line

y = 2x - 5

meets the curve

y = x^2 - 4x + 4

at exactly one point, and find the coordinates of that point.

●●●●●Level 53 marksStart

Solve the simultaneous equations

x^2 + y^2 = 52

y = x - 2

Give your answers as coordinate pairs.

●●●●●Level 54 marksStart

Solve the simultaneous equations

x + y = 7

y = x^2 - 5x + 10

●●●●●Level 54 marksStart

Show that the line

y = 4x - 9

meets the curve

y = x^2 - 2x

at exactly one point, and find the coordinates of that point.

●●●●●Level 54 marksStart

Solve algebraically the simultaneous equations

2x^2 + 3y^2 = 35

2x - y = 7

●●●●●Level 55 marksStart