Question

. Find the value of P, the system of equations Px + 3y = 1, 12x + Py = 2 has no solution.​

Answer 1

Given : , the system of equations Px + 3y = 1, 12x + Py = 2 has no solution.​

To Find : value of P

Solution:

a₁x+ b₁y=c₁

a₂x+b₂y=c₂

Consistent

if a₁/a₂ ≠ b₁/b₂  ( unique solution)

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

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution)

Px + 3y = 1,

12x + Py = 2

=> P/12  = 3/P  ≠  1/2

P/12  = 3/P

=> P² = 36

=> P = ± 6

case 1

P = 6

6/12 = 3/6  = 1/2  infinite solution

case 1

P = -6

-6/12 = 3/-6  ≠1/2  no solution

value of P is - 6

the system of equations Px + 3y = 1, 12x + Py = 2 has no solution.​

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