In order to solve the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them? \( 2 x-4 y=5 \) \( 6 x-3 y=10 \) A. Multiply the top equation by -3 . B. Multiply the top equation by -3 and the bottom equation by 2 . C. Multiply the top equation by 3 and the bottom equation by 4 . D. Multiply the top equation by -2 .

Let's consider option B – if you multiply the top equation \(2x - 4y = 5\) by -3 and the bottom equation \(6x - 3y = 10\) by 2, you'll get: - Top equation: \( -6x + 12y = -15 \) - Bottom equation: \( 12x - 6y = 20 \) Now when you add them together, \( -6x + 12y + 12x - 6y \) simplifies perfectly, letting you eliminate \(x\)! So, make sure to use the right coefficients for a smooth elimination process. If you consider the first equation multiplied by -3, while trying other options, be cautious of the coefficients. It's easy to accidentally create different terms that don't cancel out. Always keep track of how the changes affect both equations, ensuring one variable vanishes upon addition!