To find the value of y, we need to solve the equation that represents the relationship between the given line segments RS, ST, and RT.
Given:
RS = 7y + 4
ST = 4y + 7
RT = 66
To solve for y, we can set RS + ST equal to RT since the line segments add up to form a whole line.
RS + ST = RT
Substituting the given values, we have:
(7y + 4) + (4y + 7) = 66
Now, we can simplify and solve for y:
7y + 4 + 4y + 7 = 66
11y + 11 = 66
11y = 66 - 11
11y = 55
y = 55/11
y = 5
Therefore, the value of y is 5.