Question

Question 2 (i)
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.
5x - 4y + 8 = 0
7x + 6y - 9 = 0

Answer 1

The given equations are:

5x - 4y + 8 = 0
7x + 6y - 9 = 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:
$a_1=5,b_1=-4,and{c}_1=8$
$a_2=7,b_2=6and{c}_2=-9$

$\frac{a_1}{a_2}=\frac{5}{7},$

$\frac{b_1}{b_2}=\frac{-4}{6}$ and

$\frac{c_1}{c_2}=\frac{8}{-9}$

Hence, $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Therefore, the lines representing the given pair of linear equations intersect at a point.