Question

The given figure shows the path of two balls.

If path followed by the blue ball and the red ball is 2x-5y=4, and 3x-ky=6 respectively.


Determine the nature of linear equations of the given paths. Provided k=7.

• A. Coinciding
• B. Parallel
• C. Intersecting
• D. Parallel or coinciding

Answer 1

The correct option is C Intersecting

Given 2x-5y=4, and 3x-7y=6
Here, $a_1=2,b_1=-5,c_1=-4$
and $a_2=3,b_2=-7,c_2=-6$

$\frac{a_1}{a_2}=\frac{2}{3}$
$\frac{b_1}{b_2}=\frac{-5}{-7}$
$\frac{c_1}{c_2}=\frac{-4}{-6}$
$\frac{2}{3}\ne \frac{-5}{-7}$ (i.e. $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$)
so, the nature of the given linear equations is intersecting.