Question

if the system of equations (k-3)x+3y=2k and 2x+(k-4)y=8 has infinitely many solutions, then the value of k is

A. 1 only
B. 6 only
C. 1 and 6
D. 5 only

Answer 1

Answer:

6

Step-by-step explanation:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

if the system of equations (k-3)x+3y=2k and 2x+(k-4)y=8 has infinitely many solutions, then the value of k is

A. 1 only

B. 6 only

C. 1 and 6

D. 5 only

EVALUATION

Here it is given that the system of equations (k-3)x+3y=2k and 2x+(k-4)y=8 has infinitely many solutions

So by the given condition

$\displaystyle \sf{ \frac{k - 3}{2} = \frac{3}{k - 4} = \frac{2k}{8} }$

Now

$\displaystyle \sf{ \frac{k - 3}{2} = \frac{3}{k - 4} \: \: gives }$

$\displaystyle \sf{ {k}^{2} - 7k + 12 = 6}$

$\displaystyle \sf{ \implies {k}^{2} - 7k +6 = 0}$

$\displaystyle \sf{ \implies (k - 1)(k - 6) = 0}$

$\displaystyle \sf{ \implies k = 1 \: ,\: 6} \: \: - - (1)$

Again

$\displaystyle \sf{ \frac{k - 3}{2} = \frac{2k}{8} }$

$\displaystyle \sf{ \implies \: 8k - 24 = 4k }$

$\displaystyle \sf{ \implies \: 4k = 24 }$

$\displaystyle \sf{ \implies \: k = 6 \: \: \: \: - - - (2) }$

From Equation 1 and 2 we get k = 6

FINAL ANSWER

Hence the correct option is B. 6 only

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