Question

Show that the paths represented by the equations x-3y=2 and -2x+6y=5 are parallel

Answer 1

Given equations :-

» x - 3y = 2

» -2x + 6y = 5

there are three pairs of lines when solved graphically.

first one is intersecting lines. second parallel and third coincident lines.

we can easily identity by this formula :-

if a1/a2 ≠ b1/b2 then the lines are intersecting

if a1/a2 = b1/b2 ≠ c1/c2, then the lines are parallel

if a1/a2 = b1/b2 = c1/c2, then the lines are coincident.

note that :-

a1 and a2 are the coefficient of the first term of the equations respectively, b1 and b2 are the coefficient of the second term and c1 and c2 the coefficient of the third one.

here,

a1 = 1 , a2 = -2

b1 = -3 , b2 = 6

c1 = -2 , c2 = -5

➡ a1/a2 = 1/-2 = -1/2

➡ b1/b2 = -3/6 = -1/2

➡ c1/c2 = -2/-5 = 2/5

a1/a2 = b1/b2 ≠ c1/c2

hence the lines are parallel.