Using the elimination method to eliminate the y variable, what is your first step to solve the system of equations? 2x + 4y = 16 2x - 4y = 0. multiply the top equation by 4 add the equations together substitute 2x-4y in for x in the top equation multiply the bottom equation by 2

Answer 1

To eliminate the \( y \) variable in the given system of equations:

1. Equations: \[ \text{(1)} \quad 2x + 4y = 16 \] \[ \text{(2)} \quad 2x - 4y = 0 \]

The best approach is to align the coefficients of \( y \) so that they can cancel each other out when added or subtracted.

Steps to Eliminate \( y \):

1. Add the two equations together: Notice that the coefficients of \( y \) in equation (1) and equation (2) are \( 4y \) and \( -4y \), which are opposites. When added together, they will cancel out.

Therefore, the correct first step is:

• Add equations (1) and (2): \[ \begin{align*} (2x + 4y) + (2x - 4y) &= 16 + 0 \ 4x &= 16 \ x &= 4 \end{align*} \]

After finding \( x \), you can substitute it back into either original equation to find \( y \).

So, the choice to add the equations together to eliminate \( y \) is the correct first step.