For what value of c,


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


The given linear equation is 2x + cy= 8. …(i)

Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y.

Put y = x in Eq. (i), we get

$2 x+c x=8$

$\Rightarrow$ $c x=8-2 x$

$\Rightarrow$ $c=\frac{8-2 x}{x}, x \neq 0$

Hence, the required value of $c$ is $\frac{8-2 x}{x}$.

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