Question

If Kx+My+4=0 and 2x+y+1=0 then what is the value of K & M​

Answer 1

Answer:

Step-by-step explanation:

Kx+My+4=0......(1)

2x+y+1=0.........(2)

Generally, it can be expressed as

ax+by+c=0

For (1) and (2) to be similar,

The coefficients of (1) must be multiples of (2) or vice-versa.

Thus,

On comparing (1) and (2),

4/1=M/1=K/2

From above, we see that

M/1=4 => M=4

and K/2=4 => K=8

Therefore,

K=8

M=4

Answer 2

The value of K and M in terms of y is K = $\frac{2My + 8}{y+1}$ M = $\frac{K(y+1) - 8}{2y}$ and if we take values of x = -1 and y = 1, then the value of K = M + 4.

Step-by-step explanation:

Kx + My + 4 = 0  (i)

2x + y + 1 =0   (ii)

We can use the elimination method, to delete one variable and using that find the value of the other.

Thus, multiplying, equation (i) by 2 and equation (ii) by K, we obtain,

2Kx + 2My + 8 = 0  

2Kx + Ky + K = 0

Now subtracting both equations, we obtain,

2Kx + 2My + 8 - (2Kx + Ky + K) = 0

2Kx + 2My + 8 - 2Kx - Ky - K = 0

2My + 8 - Ky - K = 0

2My -Ky + 8 - K = 0

2My +8 = Ky + K

2My + 8 = K(y+1)       (iii)

K = $\frac{2My + 8}{y+1}$

From (iii), 2My = K(y+1) - 8

M = $\frac{K(y+1) - 8}{2y}$

OR

Let in equation (ii), y = 1, then equation becomes, 2x + 1 + 1 =0

or, 2x + 2= 0

or, 2x = -2

or, x = -1

Substituting value of x and y obtained above in equation (i), we get

Kx + My + 4 = 0

or, K(-1) + M(1) + 4 = 0

or -K + M + 4 = 0

or, -K + M = -4

or, -K = -4 - M

or, K = 4 + M.