Question

Show that the system equations

2x - 3y = 5,

6x - 9y = 15

has an infinite number of solutions

Answer 1

The given system of equations: 

2x - 3y = 5 

⇒ 2x - 3y – 5 = 0 ….(i) 

6x - 9y = 15 

⇒6x - 9y - 15 = 0 …(ii) 

These equations are of the following forms: 

a1x+b1y+c1 = 0, a2x+b2y+c2 = 0 

Here, a1 = 2, b1= -3, c1 = -5 and a2 = 6, b2 = -9, c2 = -15

Hence, the given system of equations has an infinite number of solutions.