For what value of c the linear equation 2x Cy 8 has equal values of x andy for its solution?

Answer

Hint: Put $x = y$ in the given equation, $2x + cy = 8$, then solve the equation to find the value of c.Complete step-by-step answer: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-$2x + cx = 8$Solving further, take x common, we get-$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, $2x + cy = 8$.So, we can also say that c should not be equal to 2.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.

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.

Given: y = x is a solution to the equation 2x + cy = 8

Put x = y

We have: 2y + cy = 8

Or, cy = 8 − 2y

c = `8/y - 2 = 8/x - 2`

Concept: Solution of a Linear Equation

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