x + 2 y = 6 x - 2 y = 4 The solution to the

Choice B is correct. Adding the first equation to the second equation in the given system yields $\left(x+2y\right)+\left(x-2y\right)=6+4$, or $\left(x+x\right)+\left(2y-2y\right)=10$. Combining like terms in this equation yields $2x=10$. Dividing both sides of this equation by $2$ yields $x=5$. Thus, the value of $x$ is $5$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the value of $2x$, not $x$.