Question

Question 2 (ii)
On comparing the ratios $\frac{a_1}{a_2}$ , $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ , 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 1

9x + 3y + 12 = 0
18x + 6y + 24 = 0
Comparing these equations with $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, we get
$a_1=9,b_1=3,and{c}_1=12$
$a_2=18,b_2=6and{c}_2=24$

$\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$ and

$\frac{c_1}{c_2}=\frac{12}{24}=\frac{1}{2}$

Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore, the lines representing the given pair of linear equations are coincident.