x/2 + y/3 = 4; x/4 + y/6 = 2

(vi) x/2 + y/3 = 4; x/4 + y/6 = 2

Sol. x/2 + y/3 = 4

Multiplying the equation with 6, we get

3x + 2y = 24

Comparing with a1x + b1y = c1 we get, a1 = 3, b1 = 2, c1 = 24

x/4 + y/6 = 2

Multiplying the equation with 12, we get

3x + 2y = 24

Comparing with a2x + b2y = c2 we get, a2 = 3, b2 = 2, c2 = 24

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

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

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

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

a₁/a₂ = b₁/b₂ = c₁/c₂

∴ Infinitely Many Solutions.