Question

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

Answer 1

The given linear equation is $2x+cy=8.$
Now, by condition, x and y-coordinate of given linear equation are same, i.e., $x=y.$
Putting $y=x$ in Eq. $\left(i\right)$, we get
$2x+cx=8$
$\Rightarrow cx=8-2x$
$\Rightarrow c=\frac{8-2x}{x},x\ne 0$
Hence, the required value of $c$ is $\frac{8-2x}{x}$.