On comparing the ratios a1/a2, b1/b2 and c1/c2 and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
6x - 3y + 10=0 and 2x -y + 9=0

To determine whether the lines represented by the equations intersect at a point, are parallel, or coincide, we need to compare the ratios of the coefficients of x, y, and the constants in both equations.

We have the two equations:

6x - 3y + 10 = 0
2x - y + 9 = 0
The general form of a linear equation is Ax + By + C = 0, where A, B, and C are the coefficients of x, y, and the constant, respectively.

For the first equation (6x - 3y + 10 = 0), we have:
A1 = 6, B1 = -3, C1 = 10

For the second equation (2x - y + 9 = 0), we have:
A2 = 2, B2 = -1, C2 = 9

Now, we compare the ratios of the coefficients:

A1/A2 = 6/2 = 3
B1/B2 = -3/-1 = 3
C1/C2 = 10/9
If the ratios of the coefficients of x and y (A1/A2 and B1/B2) are equal, but the ratio of the constants (C1/C2) is different, the lines are parallel.

In this case:

A1/A2 = 3 and B1/B2 = 3, which means the lines have the same slope.
C1/C2 = 10/9, which is not equal to 1.
Since the ratios of the coefficients of x and y are equal but the ratio of the constants is not, the lines are parallel.