On comparing the ratios `(a_(1))/(a_(2)), (b_(1))/(b_(2)) and (c_(1))/(c_(2))`, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
`9x+ 3y+ 12= 0`
`18x+ 6y + 24=0`

Answer

To determine whether the lines represented by the given pair of linear equations intersect at a point, are parallel, or are coincident, we will compare the ratios of the coefficients of the equations.

The given equations are:
1. \( 9x + 3y + 12 = 0 \) (Equation 1)
2. \( 18x + 6y + 24 = 0 \) (Equation 2)

We can rewrite these equations in the standard form \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \):

- For Equation 1:
- \( a_1 = 9 \)
- \( b_1 = 3 \)
- \( c_1 = 12 \)

- For Equation 2:
- \( a_2 = 18 \)
- \( b_2 = 6 \)
- \( c_2 = 24 \)

Now, we will calculate the ratios \( \frac{a_1}{a_2} \), \( \frac{b_1}{b_2} \), and \( \frac{c_1}{c_2} \):

1. Calculate \( \frac{a_1}{a_2} \):
\[ \frac{a_1}{a_2} = \frac{9}{18} = \frac{1}{2} \]

2. Calculate \( \frac{b_1}{b_2} \):
\[ \frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2} \]

3. Calculate \( \frac{c_1}{c_2} \):
\[ \frac{c_1}{c_2} = \frac{12}{24} = \frac{1}{2} \]

Now we compare the ratios:
\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = \frac{1}{2} \]

Since all three ratios are equal, we conclude that the lines represented by the equations are coincident lines.

### Summary of the Solution:
- The lines represented by the equations \( 9x + 3y + 12 = 0 \) and \( 18x + 6y + 24 = 0 \) are coincident.