3y = 2 – x; 3x = 6 – 9y

(ii) 3y = 2 – x; 3x = 6 – 9y

Sol. 3y = 2 – x

∴  x + 3y = 2

Comparing with a1x + b1y = c1 we get, a1 = 1, b1 = 3, c1 = 2

3x = 6 – 9y

∴  3x + 9y = 6

Comparing with a2x + b2y = c2 we get, a2 = 3, b2 = 9, c2 = 6

a₁/a₂ = 1/3 = 1/3 ............ eq. no. (i)

b₁/b₂ = 3/9 = 1/3 ............ eq. no. (ii)

c₁/c₂ = 2/6 = 1/3 ............ eq. no. (iii)

From Equation (i) , (ii) and (iii) we get

a₁/a₂ = b₁/b₂ = c₁/c₂

∴ Infinitely Many Solutions.