Question

26. What is the value of k, if the value of D, for the equations 3x+y=1 and 2x — ky=3 is 7? (A) 22 (B) – 22 (C) 11 (D) – 11​

Answer 1

Answer:

The value of k is - 3.

Step-by-step-explanation:

The given linear equations are

3x + y = 1 - - - ( 1 )

2x - ky = 3 - - - ( 2 )

We have given that,

The value of determinant of coefficients of x and y ( D ) is 7.

We have to find the value of k.

Now,

3x + y = 1 - - - ( 1 )

Comparing with a₁x + b₁y = c, we get,

• a₁ = 3
• b₁ = 1

Now,

2x - ky = 3 - - - ( 2 )

Comparing with a₂x + b₂y = c, we get,

• a₂ = 2
• b₂ = - k

We know that,

The determinant of coefficients of variables of two linear equations is given by

D = $\displaystyle{\huge{|}}$ a₁ $\qquad$ b₁ $\displaystyle{\huge{|}}$

$\quad$ $\displaystyle{\huge{|}}$ a₂ $\qquad$ b₂ $\displaystyle{\huge{|}}$

$\displaystyle{\implies}$ 7 = $\displaystyle{\huge{|}}$ 3 $\qquad$ 1 $\displaystyle{\huge{|}}$

$\qquad\qquad$ $\displaystyle{\huge{|}}$ 2 $\qquad$ - k $\displaystyle{\huge{|}}$

$\displaystyle{\implies}$ 7 = [ 3 * ( - k ) ] - ( 1 * 2 )

$\displaystyle{\implies}$ - 3k - 2 = 7

$\displaystyle{\implies}$ - 3k = 7 + 2

$\displaystyle{\implies}$ - 3k = 9

$\displaystyle{\implies\sf\:k\:=\:-\:\cancel{\dfrac{9}{3}}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:k\:=\:-\:3\:}}}}$

∴ The value of k is - 3.