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This image contains a math problem about solving systems of linear equations. Here’s a breakdown of the tasks:

1. Solve the first system using Cramer's Rule.

   • System 1: \[ \begin{align*} 2x_1 - 3x_2 + x_3 &= 1, \\ 3x_1 + 4x_3 &= 4, \\ 5x_1 + 2x_2 + x_3 &= 7. \end{align*} \]

2. Verify the solution with the inverse matrix method.

3. Solve the second system using Gaussian elimination.

   • System 2: \[ \begin{align*} 2x_1 - x_2 + x_3 &= 2, \\ 5x_2 + x_3 &= -1, \\ 3x_1 + 2x_2 + x_3 &= 1. \end{align*} \]

Would you like a detailed solution for each system?