y - 9 x = 13 5 x = 2 y What is the solution x

Choice C is correct. Adding $9x$ to both sides of the first equation in the given system yields $y=9x+13$. Substituting the expression $9x+13$ for $y$ in the second equation in the given system yields $5x=2\left(9x+13\right)$. Distributing the $2$ on the right-hand side of this equation yields $5x=18x+26$. Subtracting $18x$ from both sides of this equation yields $-13x=26$. Dividing both sides of this equation by $-13$ yields $x=-2$. Substituting $-2$ for $x$ in the equation $y=9x+13$ yields $y=9\left(-2\right)+13$, or $y=-5$. Therefore, the solution $\left(x,y\right)$ to the given system of equations is $\left(-2,-5\right)$.

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

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

Choice D is incorrect. This is the solution $\left(y,x\right)$, not $\left(x,y\right)$, to the given system of equations.