Question

Simultaneous equations:
Find two numbers whose difference is 5 and whose sum is 11.

Answer 1

x=8 ; y=3

Explanation:

suppose,

one of the number is x

other one is y ; x>y

according to the question,

x-y =5........(1)

x+y=11.........(2)

(2)+(1)=>

x+y+x-y=11+5

2x=16

x=8 [divided by 2 on both side]

then,

(2)-(1)=>

x+y-x+y=11-5

2y=6

y=3 [divided by 2 on both side]

Answer 2

8 and 3

Explanation:

Let x and y be the 2 numbers with x > y, then

x - y = 5 → (1)

x + y = 11 → (2)

Add the 2 equations together term by term to eliminate y

2x = 16 ( divide both sides by 2 )

x = 8

Substitute x = 8 into (2)

8 + y = 11 ( subtract 8 from both sides )

y = 3

The 2 numbers are 8 and 3