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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

$\frac{14 x}{7 y} = 2 w + 19$

The given equation relates the distinct positive real numbers $w$ , $x$ , and $y$ . Which equation correctly expresses $w$ in terms of $x$ and $y$ ?

ExplanationShow

Choice C is correct. Dividing each side of the given equation by $2$ yields $\frac{14 x}{14 y} = \frac{2 w + 19}{2}$ , or $\frac{x}{y} = w + 19$ . Because it's given that each of the variables is positive, squaring each side of this equation yields the equivalent equation $(\frac{x}{y})^{2} = w + 19$ . Subtracting $19$ from each side of this equation yields $(\frac{x}{y})^{2} - 19 = w$ , or $w = (\frac{x}{y})^{2} - 19$ .

Choice A is incorrect. This equation isn't equivalent to the given equation.

Choice B is incorrect. This equation isn't equivalent to the given equation.

Choice D is incorrect. This equation isn't equivalent to the given equation.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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