The graphs of the equations 7x+y = 7 and x+6y = -48 intersect at a single point and the correct option is C.
To determine without graphing whether the graphs of the two given equations are identical lines, parallel lines, or lines intersecting at a single point, we can use the following steps:
1. Solve both equations for y.
Equation 1:
7x + y = 7
y = -7x + 7
Equation 2:
x + 6y = -48
6y = -x - 48
y = -1/6x - 8
2. Compare the slopes and y-intercepts of the two equations.
Equation 1: Slope = -7, y-intercept = 7
Equation 2: Slope = -1/6, y-intercept = -8
Since the slopes are different, the two lines are not identical nor parallel. Therefore, the graphs of the two lines must intersect at a single point and the correct option is C.