Simultaneous equations

The Maths Habit
Walkthrough to printWalkthrough: multiply first

Solve

4m = 10m = 2.5

2 + 3m = 14m = 4

3d + 5 = 26d = 7

Work out the price of a doughnut.£2

Work out the price of a milkshake.£3

Write how you worked this out using equations.

3d + 2m = 122d + 2m = 10

Work out the price of a doughnut.£3

Work out the price of a milkshake.£2.50

Write how you worked this out using equations.

3d + 4m = 192d + 4m = 16

Work out the price of a milkshake.£2.50

Work out the price of a doughnut.£1.50

Write how you worked this out using equations.

4d + 3m = 13.54d + 2m = 11

Work out the price of a milkshake.£1.50

Work out the price of a doughnut.£2.50

Write how you worked this out using equations.

2d + 3m = 9.52d + m = 6.5

is now dis now m

dddddmm= £13
dddmm= £9

Work out d.d = 2

Work out m.m = 1.5

Write each row as an equation.

5d + 2m = 133d + 2m = 9

3d + 2m = £14d + 2m = £8

Find d and m.

d = £3, m = £2.50
2d + 5m = £14.502d + 3m = £9.50

Find d and m.

d = £1, m = £2.50
4d + m = 17d + m = 8

Find d and m.

d = 3, m = 5

Simultaneous equations
Two equations that are both true at the same time.

3x + y = 13x + y = 7

xxxy= 13
xy= 7

4x + y = 222x + y = 12

3x + 2y = 17x + 2y = 11

4x + y = 19x + y = 7

x = 4   y = 3

xxxxy= 19
xy= 7

extra tiles = 19 − 7 = 12

5x + 2y = 312x + 2y = 16

x = 5   y = 3

4x + y = 19x + y = 7

x = 4   y = 3

6x + y = 322x + y = 12

x = 5   y = 2

Simultaneous equations worksheet, page 1

Simultaneous equations worksheet, page 2

Answer sheet

  1. 3 pens and 2 rulers cost £3.10. 1 pen and 2 rulers cost £1.90. Find the cost of a pen and the cost of a ruler.

    60p and 65p

  2. Solve 3x + y = 14 and 2x − y = 6.

    x = 4, y = 2

  3. Solve 5x + 4y = 3 and 5x + y = 12.

    x = 3, y = −3

  1. Solve 5x + y = 26 and 2x + y = 11

    x = 5, y = 1

  2. Solve 3x + 4y = 25 and 3x + y = 13

    x = 3, y = 4

  3. Solve 2x + 3y = 4 and 2x + y = 8

    x = 5, y = −2
Exit tickets to print