Question

Find the value of p, for which the system of equations have infinitely many solutions: x - py = 2, 3x + 6y = -6
3
-2
2
-3​

Answer 1

Answer:

c = 2

Step-by-step explanation:

a1 = 1 , b1 = -p , c1 = 2

a2 = -3 , b2 = 6 , c2= -

infinite many solution

a1 = b1 = c1

__ __ __

a2 b2 c2

1 = -p = 2

__ ____ ____

-3 6 -6

1 = -p

__ ____

-3 6

6 = (- p) x (-3 )

6 = 3p

p = 6 / 3

p = 2

I hope this will help you

Answer 2

Answer:-

According to the Question

It is given that ,

Equation 1st

→ x - py -2 = 0

• a₁ = 1 , b₁ = -p & c₁ = -2

Equation 2nd

→ 3x + 6y +6 = 0

• a₂ = 3 , b₂ = 6 & c₂ = 6

The system of equation have infinitely many solution .

Condition for infinitely many solution

• a₁/a₂ = b₁/b₂ = c₁/c₂

Substitute the value we get

$\longrightarrow$ 1/3 = -p/6 = -2/6

$\longrightarrow$ -3p = 6 or -6p = -12

$\longrightarrow$ p = -6/3 or 6p = 12

$\longrightarrow$ P = -2 or p = 12/6

$\longrightarrow$ P = -2 or P = 2

• Hence, the value of p = -2 or 2 .