Question

if the lines representing linear equations 2x-1y+3=0and 6x-3y=k are coincide, then the value of "k" (a) -3 (b) -9 (c) 3 (d) 9​

Answer 1

Answer:

The value of k is 9.

Option d)

Step-by-step-explanation:

The given linear equations are

2x - y + 3 = 0 $\qquad$ - - - ( 1 ) &

6x - 3y = k $\qquad$ - - - ( 2 )

We have to find the value of k.

Now,

2x - y + 3 = 0 $\qquad$ - - - ( 1 )

Comparing with ax + by + c = 0, we get,

• a₁ = 2
• b₁ = - 1
• c₁ = 3

Also,

6x - 3y = k $\qquad$ - - - ( 2 )

Comparing with ax + by + c = 0, we get,

• a₂ = 6
• b₂ = - 3
• c₂ = k

We know that,

For two coincident lines,

$\displaystyle{\pink{\sf\:\dfrac{a_1}{a_2}\:=\:\dfrac{b_1}{b_2}\:=\:\dfrac{c_1}{c_2}}}$

$\displaystyle{\implies\sf\:\dfrac{b_1}{b_2}\:=\:\dfrac{c_1}{c_2}}$

$\displaystyle{\implies\sf\:\dfrac{-\:1}{-\:3}\:=\:\dfrac{3}{k}}$

$\displaystyle{\implies\sf\:\dfrac{1}{3}\:=\:\dfrac{3}{k}}$

$\displaystyle{\implies\sf\:k\:\times\:1\:=\:3\:\times\:3}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:k\:=\:9\:}}}}$

∴ The value of k is 9.

Answer 2

The given linear equations are

2x - y + 3 = 0 _____(1) &

6x - 3y = k ____(2)

We have to find the value of k.

Now,

2x - y + 3 = 0 ____(1)

Comparing with ax + by + c = 0, we get,

a₁ = 2

b₁ = - 1

c₁ = 3

Also,

6x - 3y = k ___(2)

Comparing with ax + by + c = 0, we get,

a₂ = 6

b₂ = - 3

c₂ = -k

We know that,

For two coincident lines,

a₁/a₂ = b₁/b₂ = c₁/c₂

b₁/b₂ = c₁/c₂

so ,

-1/-3 = 3/-k

k = 3 × -3 = -9

• value of k = -9