To solve the system of equations using elimination, we need to manipulate one or both equations so that one of the variables cancels out when we add or subtract the equations. The system is:

‒6x + 4y = 26
5x + 2y = 37

To eliminate a variable, the coefficients of either $x$ or $y$ in both equations should be opposites.

Let's focus on eliminating $y$. In the first equation, the coefficient of $y$ is 4, and in the second equation, the coefficient is 2. To make these coefficients opposites, we need to make them the same but with opposite signs.

1. If we multiply the second equation by -2, the $y$ terms will become opposites: $5x + 2y = 37 \quad \text{(multiply by -2)} \quad -10x - 4y = -74$ Now we can add this to the first equation: $(-6x + 4y) + (-10x - 4y) = 26 + (-74)$ $-16x = -48$ Therefore, the correct option is D. Multiply the second equation by -2.

Would you like to see a detailed solution for this system? Here are some related questions to expand on this concept:

1. How do you solve a system of equations using substitution?
2. What are the conditions for a system of equations to have no solutions or infinitely many solutions?
3. What happens if both equations are multiples of each other in a system?
4. Can elimination be applied if both equations are nonlinear?
5. What is the difference between solving systems graphically and algebraically?

Tip: Always check if scaling either of the equations will simplify the elimination process before using substitution or other methods.