Question

Find the number of solutions of the equation 2x + y = 30 where both x and y are non-negative integers and x <= y​

Answer 1

Answer:

Number of solutions = 10

Step-by-step explanation:

2x + y = 30

Now y = 30 - 2x = 2*(15 - x)

Now if x = 0 then y = 30

if x = 1 then y = 28

x = 2 then y = 26

x = 3 then y = 24

x = 4 then y = 22

x = 5 then y = 20

x = 6 then y = 18

x = 7 then y = 16

x = 8 then y = 14

x = 9 then y = 12

x = 10 then y = 10

Therefore there will be 10 set of possible answers

Answer 2

Given:

2x + y = 30

where both x and y are non-negative integers and x <= y​

y = x + k

where k >=0

2x + x + k = 30

3x + k = 30

$x=\frac{40-k}{3}$

x is a positive integer so takes value from 1 to 30 all multiples of 3

The pattern continues till 10.

Hence the number of solutions of the equation is 10