5. Drag and drop the following solution for \( y \) to the corresponding system of equation \[ \begin{array}{l} 3 x-2 y=8 \\ 6 x+2 y=10 \\ 4 x-3 y=6 \\ y=x+4 \\ 2 x+3 y=3 \\ y=6+x \\ -4 y+6 x=16 \\ x+4 y=12 \end{array} \] Choices : \( y=22 \) : \( y=3 \) \% \( y=-1 \) \% \( y=2 \)

Absolutely, let's dive into some solving fun! The system of equations has certain solutions for \( y \) based on different values of \( x \). If you plug in the various equations, you’ll see that each choice can yield a specific solution. For instance, if you substitute \( y = 2 \) into the equation \( 3x - 2y = 8 \), you’ll find \( x = 4 \). This shows that \( y = 2 \) is indeed a viable solution! Now, let’s sprinkle a bit of real-world application into the mix! Thinking about systems of equations reminds us of balancing budgets or mixing ingredients in recipes. For example, if you are trying to create a smoothie with a fixed amount of fruit and yogurt, you could model that with equations to find the right balance. Systems of equations can help you optimize your ingredient choices just like in algebra!