Option E
The sum of all possible values of y is 20
Solution:
Given that,
6x + 2y = 25
Where, xy > 0
We have to find the sum of all possible values of y if x is a positive integer
We can use values of x = 1, 2, 3, 4
For x = 5 and above, y will be negative
Substitute x = 1 in given equation
6(1) + 2y = 25
6 + 2y = 25
2y = 25 - 6
2y = 19
Divide both the sides of equation by 2
[tex]y = \frac{19}{2}[/tex]
Substitute x = 2 in given equation
6(2) + 2y = 25
2y = 25 - 12
2y = 13
Divide both the sides of equation by 2
[tex]y = \frac{13}{2}[/tex]
Substitute x = 3 in given equation
6(3) + 2y = 25
2y = 25 - 18
2y = 7
Divide both the sides of equation by 2
[tex]y = \frac{7}{2}[/tex]
Substitute x = 4 in given equation
6(4) + 2y = 25
24 + 2y = 25
2y = 25 - 24
2y = 1
Divide both the sides of equation by 2
[tex]y = \frac{1}{2}[/tex]
Now add all the values of "y"
[tex]\text{Sum of possible values of y } = \frac{19}{2} + \frac{13}{2} + \frac{7}{2} + \frac{1}{2}\\\\\text{Sum of possible values of y } = \frac{19+13+7+1}{2}\\\\\text{Sum of possible values of y } = \frac{40}{2}=20[/tex]
Thus sum of all possible values of y is 20
