In a logistics planning scenario, an analyst models two delivery routes using the system of equations \left\{\frac{1}{3}x - \frac{1}{2}y = 1,\; \frac{3}{4}x - y = \frac{5}{2} ight\}. Arrange the following steps of the elimination method in the correct procedural order to determine the values of $x$ and $y$.

A supply chain coordinator is analyzing shipping routes modeled by the system of equations $\left\{\frac{1}{3}x - \frac{1}{2}y = 1,\; \frac{3}{4}x - y = \frac{5}{2}\right\}$. When using the elimination method, what is the appropriate first step to clear the fractions from these specific equations?

A project manager uses a resource allocation model defined by the system of equations $\left\{\frac{1}{3}x - \frac{1}{2}y = 1,\; \frac{3}{4}x - y = \frac{5}{2}\right\}$. Match each procedural milestone of the elimination method with its corresponding mathematical result.

A manufacturing supervisor uses the system $\left\{\frac{1}{3}x - \frac{1}{2}y = 1,\; \frac{3}{4}x - y = \frac{5}{2}\right\}$ to calculate the required weights of two raw materials. After clearing the fractions to obtain the equivalent equations ${}2x - 3y = 6$ and ${}3x - 4y = 10$, the supervisor intends to eliminate $x$ by adding the equations. If the first equation is multiplied by 3, the supervisor must multiply the second equation by ____ to create opposite coefficients for $x$.

A logistics analyst is balancing resource allocations using the system of equations $\left\{\frac{1}{3}x - \frac{1}{2}y = 1,\; \frac{3}{4}x - y = \frac{5}{2}\right\}$. True or False: When clearing the fractions in the second equation by multiplying every term by the least common denominator of 4, the resulting equivalent equation is ${}3x - 4y = 10$.