Given equation: 3x + 2y - 10 = 0

Relation between x and y:
- To find the relation between x and y, we need to rearrange the given equation in terms of x or y.
- Let's rearrange the given equation in terms of x:
3x + 2y - 10 = 0
3x = 10 - 2y
x = (10 - 2y)/3

- Now we can see that the relation between x and y is x = (10 - 2y)/3.
- This means that the value of x depends on the value of y.
- We can say that x is a function of y.

Ranges of x and y:
- Rx and Ry denote the ranges of x and y respectively.
- The range of a variable is the set of all possible values that the variable can take.
- To find Rx and Ry, we need to find the range of x and y respectively in the given equation.

Range of y:
- Let's rearrange the given equation in terms of y:
3x + 2y - 10 = 0
2y = 10 - 3x
y = (10 - 3x)/2

- Now we can see that the range of y depends on the range of x.
- To find the range of y, we need to find the range of x first.

Range of x:
- Let's write the equation in standard form:
3x + 2y = 10
- To find the range of x, we can assume different values of y and find the corresponding values of x.
- Let's assume y = 0:
3x + 2(0) = 10
3x = 10
x = 10/3
- Let's assume y = 1:
3x + 2(1) = 10
3x = 8
x = 8/3
- Let's assume y = -1:
3x + 2(-1) = 10
3x = 12
x = 4

- Now we can see that the range of x is from 4/3 to 10/3.
- We can write this as 3Rx = [4, 10].

Range of y (contd.):
- Now we can find the range of y using the range of x:
y = (10 - 3x)/2
- Let's put the minimum value of x:
y = (10 - 3(4/3))/2
y = 5/3
- Let's put the maximum value of x:
y = (10 - 3(10/3))/2
y = -1

- Now we can see that the range of y is from -1 to 5/3.
- We can write this as 2Ry = [-1, 5/3].

Relation between Rx and Ry:
- We can see that 3Rx = [4, 10] and 2Ry = [-1, 5/3].
- Multiplying the second range by 3/2, we get:
3/2 * 2Ry = [-3/2, 5/2]
- We can see that 3Rx = 2 * (3/2 * 2R