Question

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

Answer 1

Finding the value of $c$:

Given that, the given equation has equal values of $x$ and $y$ for its solution

So , on substituting $x=y$ in the equation $2x+cy=8$

$2x+cx=8$

$\Rightarrow x(2+c)=8$

$\Rightarrow 2+c=\frac{8}{x}$

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

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

Therefore, the value of $c$ is found to be $\frac{8-2x}{x},wherex\ne 0$.