Question

# For what value of c, the linear equation, $2x + cy = 8$has equal value of x and y for its solution.${\text{A}}{\text{. c = }}\dfrac{{7 - 2x}}{x},x \ne 0$${\text{B}}{\text{. c = }}\dfrac{{8 - 2x}}{x},x \ne 0$${\text{C}}{\text{. c = }}\dfrac{{13 - 2x}}{x},x \ne 0$${\text{D}}{\text{. c = }}\dfrac{{19 - 2x}}{x},x \ne 0$

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Hint: Put $x = y$ in the given equation, $2x + cy = 8$, then solve the equation to find the value of c.

According to the question, we have the equation, $2x + cy = 8 - (1)$
Now, it is asked to find the value of c for which, $x = y$.
So, put $x = y$ in equation (1), we get-
$2x + cx = 8$
$x(2 + c) = 8$
$\Rightarrow x = \dfrac{8}{{2 + c}}$
$\Rightarrow c = \dfrac{{8 - 2x}}{x}$, so the correct option is B.
Now, we know that the denominator should not be zero, so $\ 2 + c \ne 0 \\ \Rightarrow c \ne - 2 \\$
And, c=0,2,6 satisfies the condition, $2x + cy = 8$.
Note – Whenever such types of question appear, then always solve the question step by step, using the information given in the question. As mentioned in the solution, the value of c is found when $x = y$, satisfies.