A linear relationship is a relationship of the form y = mx + b, where y and x are the linear variables, m is the rate of change and b is the value of y when x = 0.
Gym A:
Let x represent the month and y represent the total cost for the gym. From the table, we can represent the values in the form (x, y) as (1,70), (2, 90) and (3, 110). We can find the relationship between x and y using the formula:
Gym B:
We can represent the values from the table as (1,55), (2, 80) and (3, 105). We can find the relationship between x and y using the formula:
To know how many solutions are in the problem, we have to solve for x and see what result we have left. According to the result, we will know how many solutions there are
8x + 47 = 8(x + 5)
8x + 47 = 8*x + 8*5
8x + 47 = 8x + 40
8x - 8x = 40 - 47
0 = -7
As we can see we are left with an equality that is not fulfilled, this means that there is no solution to the problem, at least in the field of real numbers