\( \begin{array}{l}2 x+3 y=6 \\ 5 x+2 y=4\end{array} \) Which of the following equations could be the result of multiplication and addition to eliminate a variable in the system of equations? \( \begin{array}{l}19 x=24 \\ 11 y=22\end{array} \)

To eliminate a variable in the given system of equations, you can manipulate both equations through multiplication and addition. Multiplying the first equation by 5 gives you \(10x + 15y = 30\), and multiplying the second equation by 2 results in \(10x + 4y = 8\). Subtracting these results leads to a new equation in terms of \(y\). If you look closely at the outcome of combining equations correctly, indeed \(19x=24\) could be a plausible outcome if derived from different manipulations and combinations of coefficients. However, note that \(11y=22\) simplifies to \(y=2\), which shows the value of one variable significantly if found — hence, each approach can bear varying routes to reveal valid solutions! For those looking into solving linearly independent equations, it's worth exploring methods like substitution and elimination further! Engaging with practices exemplifying real-world scenarios can enhance understanding, like optimizing delivery routes using systems of equations!