(Solved): A linear circuit can be described using the following equations where VS is an independent voltage ...

A linear circuit can be described using the following equations where VS is an independent voltage source and \( \mathrm{R} 1 \) to \( \mathrm{R} 4 \) represent resistors. \[ \text { KVL1: }\left(i_{1}-i_{2}\right) R_{1}+\left(X-i_{3}\right) R_{2}=V_{S} \] KVL2: \( \left(i_{2}-i_{3}\right) R_{3}+i_{2} R_{4}=\left(i_{1}-i_{2}\right) R_{1} \) KVL3: \( \alpha I_{x}-\left(i_{1}-i_{3}\right) R_{2}+\left(i_{3}-i_{2}\right) Y=0 \) Control Variable equation: \( I_{x}=i_{1}-i_{2} \) a. Determine \( X \) and \( Y \). b. Draw the equivalent circuit given the information provided in the equations. Justify your answers with working and comments (no working/comments, no marks).