SAT Question c8db0e19: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. It’s given that in the equation $\frac{1}{4xy}+xyz=\frac{1}{3yz}$, $x$, $y$, and $z$ are positive numbers. Multiplying both sides of this equation by the least common denominator of $12xyz$ yields $12xyz(\frac{1}{4xy}+xyz)=12xyz(\frac{1}{3yz})$, which gives $\frac{12xyz}{4xy}+12x^2{y}^2{z}^2=\frac{12xyz}{3yz}$, or $3z+12x^2{y}^2{z}^2=4x$. Subtracting $3z$ from both sides of this equation yields $12x^2{y}^2{z}^2=4x-3z$. Dividing both sides of this equation by $12x^2{z}^2$ yields $y^2=\frac{4x-3z}{12x^2{z}^2}$. Taking the square root of both sides of this equation yields $y=\pm \sqrt{\frac{4x-3z}{12x^2{z}^2}}$. Since $y$ is a positive number, the expression $\sqrt{\frac{4x-3z}{12x^2{z}^2}}$ is equivalent to $y$.