Question

$$5 x-2 y=2 y-3 x$$ $$\begin{array}{cc} \text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x & y \end{array}$$ A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

Short answer

B. Quantity B is greater.

Step-by-step solution

Simplify the given equation

To solve this problem, begin by simplifying the equation \(5x - 2y = 2y - 3x\). This can be achieved by shifting the terms based on the variable type, to one side of the equation. Add \(3x\) to both sides and \(2y\) to both sides, yielding \(5x + 3x = 2y + 2y\). This simplifies to \(8x = 4y\).

Further isolate the variables

To further simplify, divide both sides of the equation \(8x = 4y\) by \(4\), which results in \(2x = y\). This now indicates that the value of \(y\) is twice the value of \(x\) or \(x\) is half of \(y\).

Determine the value relationship between variables x and y

From the resulting equation \(2x = y\), we can infer that \(y\) is greater than \(x\), given \(x\) does not equal zero. Thus 'Quantity B' is greater than 'Quantity A'.