Explanation:

In order to determine whether the given pair of linear equations is consistent or inconsistent, we need to compare their ratios.

Step 1: Write the given pair of linear equations in the form of ax + by = c.

x + 6y = 0
3x + 3y = 18

Step 2: Find the ratio of the coefficients of x in both equations.

Ratio = 1/3

Step 3: Find the ratio of the coefficients of y in both equations.

Ratio = 6/3 = 2

Step 4: Compare the ratios.

Since the ratios of the coefficients of x and y are not equal in both equations, the given pair of equations is inconsistent.

Explanation in words:

The given pair of equations can be written in the form of ax + by = c. By comparing the ratios of the coefficients of x and y in both equations, we can determine whether they are consistent or inconsistent.

In this case, the ratio of the coefficients of x in both equations is 1/3, while the ratio of the coefficients of y is 2. Since these ratios are not equal, the given pair of equations is inconsistent.

This means that there is no solution for this system of equations, as the two lines do not intersect at any point.