x 2 + y + 7 = 7 20 x + 100 - y = 0

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 $\left(x+10\right)\left(x+10\right)=0$, or ${\left(x+10\right)}^2=0$. 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 $-10$.