Question

1 - Understanding simultaneous equations

Solve these simultaneous equations.
4 pillows and 5 quilts cost £58 W 4p + 5q = 58
6p + 59 62
6 pillows and 5 quilts cost £62
Find the cost of one of each.
p = 0 and a
q =
za + 2b = 34
za + 5b = 43
7 apple pies and 2 banoffee cost £34
7 apple pies and 5 banoffee cost £43
Find the cost of one of each.
and b​

Answer 1

1. p = 2, q = 10

2. a = 4, b = 3

Explanation:

1. $ pillows and 5 quilts cost £58.

4p + 5q = £58

6 pillows and 5 quilts cost £62.

6p + 5q = £62

So that,

4p + 5q = 58 .............. 1

6p + 5q = 62 ............. 2

Subtract equation 1 from 2

6p - 4p + 5q - 5q = 62 - 58

2p = 4

p =
`(4)/(2)`

p = 2

substitute the value of p in equation 1

4(2) + 5q = 58

8 + 5q = 58

5q = 50

q =
`(50)/(5)`

q = 10

Thus,

p = 2, q = 10

2. 7 apple pies and 2 banoffee cost £34

7a + 2b = £34

7 apple pies and 5 banoffee cost £43

7a + 5b = £43

So that,

7a + 2b = 34 ............. 1

7a + 5b = 43 ........... 2

Subtract equation 2 from 1

7a - 7a + 5b - 2b = 43 - 34

3b = 9

b =
`(9)/(3)`

b = 3

substitute the value of b in equation 1

7a + 2(3) = 34

7a + 6 = 34

7a = 28

a =
`(28)/(7)`

a = 4

Thus,

a = 4, b = 3