Question

Find the value of k if the equations 4x + 5y = 32
and 12x + 15y = 2k are not inconsistent​

Answer 1

Answer:

K = 48

Step-by-step explanation:

4x + 5y =32 ...(1)

12x + 15y = 2k ...(2)

Multiplying equation (1) by 3 we get

12x + 15y = 96. ...(3)

Now substract equation (2) from equation (3) we get

96 - 2k = 0

96 = 2k

K = 48

Answer 2

Given,

Equation of 2 lines are 4x + 5y = 32

and 12x + 15y = 2k

To Find,

Value of k = ?

Solution,

Lets 4x + 5y - 32 = 0 be equation 1 and  12x + 15y - 2k = 0 be equation 2.

The equations are in the form $a_1x+b_1y+c_1 =0,a_2x+b_2y+c_2 =0$ where

$a_1 = 4, b_1 = 5 , c_1 = -32$  and $a_2 = 12, b_2 = 15 , c_2 = -2k$

We know that conditions for the linear equations to be inconsistent are

$(a_1/a_2)=(b_1/b_2)\neq (c_1/c_2)$

Putting values in this equation we get,

(4/12) = (5/15) ≠ (-32/-2k)

(1/3) = (1/3) ≠ (16/k) [first condition is true as 1/3 = 1/3]

16/ k ≠ 1/3

By cross multiplying we get,

k ≠ 16*3

k ≠ 48

Hence, k should not be equal to 48. Any value of k other than 48 will make these linear equations inconsistent.