Question

on comparing the ratios a1/a2 b1/b2 c1/c2 and without drawing them, check whether the system of equations 9x+8y-15=0 and 15 x+40 y/3-25=0 intersecting at a point,parallel or coincide

Answer 1

Given Equations :

• 9x + 8y - 15 = 0
• 15x + 40y - 25 = 0

$\frac{a1}{a2} = \frac{9}{12}$

$\frac{b1}{b2} = \frac{8}{40} = \frac{1}{5}$

$\frac{c1}{c2} = \frac{ - 15}{ - 25} = \frac{3}{5}$

$⟹\frac{9}{12}$≠$\frac{1}{5}$≠$\frac{3}{5}$

Here,

$\frac{a1}{a2} ≠ \frac{b1}{b2}$

Which means, they are intersecting lines with one unique solution.

____________________

Thank You!