Question

4) If 7x - ky = 4, 2x + 5y = 9 and 2x + y = 8 are consistent then value of k is
185
2
a
b)
c) 185
d) 2
2
185
T11​

Answer 1

Answer:

k=185/2

Step-by-step explanation:

7x-ky=4. (1)

2x+5y=9. (2)

2x+y=8. (3)

so solving the equations 2&3 we get x=31/8 and y=1/4

putting the values of x and y in equation 1 we get

7×(31/8)-k×(1/4)=4

(217/8)-(k/4)=4

taking LCM of 8&4 we get 8 as the LCM

217-2k=32

k= (217-32)/2

k=185/2

Answer 2

The value of k = 185/2

Given :

The equations 7x - ky = 4 , 2x + 5y = 9 and 2x + y = 8 are consistent

To find :

The value of k

Solution :

Step 1 of 3 :

Write down the given system of equations

The given system of equations are

7x - ky = 4

2x + 5y = 9

2x + y = 8

Step 2 of 3 :

Form the equation to find the value of k

Here it is given that the system of equations are consistent

By the given condition

$\displaystyle\begin{vmatrix} \sf 7 & \sf- k & 4\\ 2 & 5 & 9 \\ 2 & 1 & 8 \end{vmatrix} = 0$

Step 3 of 3 :

Find the value of k

$\displaystyle\begin{vmatrix} \sf 7 & \sf- k & 4\\ 2 & 5 & 9 \\ 2 & 1 & 8 \end{vmatrix} = 0$

$\displaystyle \sf{ \implies 7(40 - 9) + k(16 - 18) + 4(2 - 10) = 0}$

$\displaystyle \sf{ \implies 217 - 2k - 32 = 0}$

$\displaystyle \sf{ \implies 185 - 2k = 0}$

$\displaystyle \sf{ \implies 2k = 185}$

$\displaystyle \sf{ \implies k = \frac{185}{2} }$