Substitute either equation into the other to solve. I'm going to substitute the second equation for the value of y in the first:
2x + (1/3x +1) = -6
(7/3x) + 1 = -6
7/3x = -7
The graph plots 2x + y = -6 as blue and y =1/3x +1 as orange
The system of linear equations 2x + y = -6 and y = 1/3x + 1 has to be solved.
Substitute y = x/3 + 1 in 2x + y = -6
2x + x/3 + 1 = -6
(7x)/3 = -7
x = -3
y = x/3 + 1 = 0
The solution of the system of equations is (-3, 0)
Drawing the graph of the two lines graphically shows that this is the root.