The relation between K1
and K2
for which the system of linear equations K1x + 3y = 8 and 4x + K2y = 16 represents
coincident lines, is:

Question

The relation between K1
 and K2
 for which the system of linear equations K1x + 3y = 8 and 4x + K2y = 16 represents
coincident lines, is:

Accepted Answer

Given the system of linear equations:

1) K1x + 3y = 8
2) 4x + K2y = 16

For the lines to be coincident, the ratios of the coefficients of x, y, and the constants must be equal:

(K1 / 4) = (3 / K2) = (8 / 16)

Calculate the constant ratio:  
8 / 16 = 1/2

So,  
K1 / 4 = 1/2 => K1 = 4 * 1/2 = 2   
3 / K2 = 1/2 => K2 = 3 / (1/2) = 3 * 2 = 6

Now, check the relation between K2 and K1:  
K2 = 6 and K1 = 2 => K2 = 3 * K1

Therefore, the relation for coincident lines is K2 = 3K1.

Answer

Answer

Answer