Question

On comparing the ratios a1/a2 , b1/b2 , c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

(i) 5x – 4y + 8 = 0

7x + 6y – 9 = 0​

Answer 1

Explanation:

✒ Given expressions;

5x−4y+8 = 0

7x+6y−9 = 0

➡Comparing these equations with a1x+b1y+c1 = 0

➡And a2x+b2y+c2 = 0

We get,

➡a1 = 5, b1 = -4, c1 = 8

➡a2 = 7, b2 = 6, c2 = -9

➡(a1/a2) = 5/7

➡(b1/b2) = -4/6 = -2/3

➡(c1/c2) = 8/-9

➡Since, (a1/a2) ≠ (b1/b2)

So, the pairs of equations given in the question have a unique solution and the lines cross each other at exactly one point.

Answer 2

$\huge\mathfrak\red{Answer :) }$

⟹ 5x - 4y + 8 = 0 ;

⟹ 7x + 6y - 9 = 0

We have a1 = 5 , b1 = -4 , c1 = 8 ,

⟹ a2 = 7 , b2 = 6 , c2 = -9

Now , a1/a2 = 5/7 ; b1/b2 = -4/6 = -2/3

$\huge\mathfrak\red{Therefore ,}$

⟹ a1/a2 ≠ b1/b2

⟹ So the given pair of linear equations are intersecting lines and have unique