The values of the variables x and y associated with the geometric system are 82 and 15, respectively.
How to determine the values of two variables associated with angles
In this problem we find a geometric system formed by three lines with a common point of intersection, creating pairs of opposite angles, whose equations are introduced below:
x - 67 = y
x = 5 · y + 7
Then, the resulting system of linear equations:
x - y = 67
x - 5 · y = 7
By first equation:
x = 67 + y
In the second equation:
(67 + y) - 5 · y = 7
- 4 · y = - 60
y = 15
Finally, we determine x:
x = 67 + 15
x = 82