Question

Given the linear equation 2x+3y-8=0, another linear equation is two variable such that pair so formed represent intersecting line is?​

Answer 1

Step-by-step explanation:

Given line is 2x+3y−8=0

(a)example of intersecting line ;

x+y−5=0  forms a intersecting line 

(b) example for parallel line 

Parallel line ⇒slopes must be equal 

⇒6x+9y+10=0 is parallel to the given line 

(c) example of coincident lines 

Coincident ⇒ratio of coefficient must be equal 

⇒4x+6y−16=0 coincides with the given line

Answer 2

To find another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines, it should satisfy below condition;

(a1/a2) = (b1/b2) = (c1/c2)

Thus, another equation could be 4x + 6y – 16 = 0, such that;

(a1/a2) = 2/4 = 1/2 ,(b1/b2) = 3/6 = 1/2, (c1/c2) = -8/-16 = 1/2

Clearly, you can see another equation satisfies the condition.