Question

The definite solution of the equation $Kx–C=My–C$, where K, C, M are non-zero constants, is

• A. (C,M)
• B. (C,K)
• C. (0,0)
• D. (C,K+M)

Answer 1

The correct option is C (0,0)

Given: $Kx–C=My–C$, where K, C, M are non-zero constants
$\Rightarrow Kx=My$ …..(i)
Substituting x = C and y = M in (i), we get
$KC=M\times M$
$\Rightarrow KC=M^2$ (Maybe or may not be true)
Therefore, (C, M) is not a definite solution of (i).
Substituting x = C and y = K in (i), we get
KC = MK
$\Rightarrow C=M$ (Maybe or may not be true)
Therefore, (C, K) is not a definite solution of (i).
Substituting x = 0 and y = 0 in (i), we get
$K\left(0\right)=M\left(0\right)$
$\Rightarrow 0=0$ (Always true)
Therefore, (0, 0) is a definite solution of (i).
Substituting x = C and y = K + M in (i), we get
$KC=M(K+M)$
$\Rightarrow KC=KM+M^2$ (Maybe or may not be true) Therefore, (C, K + M) is not a definite solution of (i).
Hence, the correct answer is option (c).