The correct answer is $-10$ . Adding $y$ to both sides of the second equation in the given system yields $20x+100=y$. Substituting $20x+100$ for $y$ in the first equation in the given system yields $x^2+20x+100+7=7$. Subtracting 7 from both sides of this equation yields $x^2+20x+100=0$. Factoring the left-hand side of this equation yields $(x+10)(x+10)=0$, or $(x+10)^2=0$. Taking the square root of both sides of this equation yields $x+10=0$. Subtracting 10 from both sides of this equation yields $x=-10$. Therefore, the value of $x$ is $-10$.