Questions: x1-x2 = 1 -2 x1+3 x2 = -4

Solution Steps

To solve the system of linear equations, we can use matrix operations or substitution/elimination methods. Here, we will use the numpy library in Python to solve the system of equations by representing it in matrix form and then using numpy's linear algebra solver.

We start with the given system of equations: \[ \begin{aligned} x_{1} - x_{2} & = 1 \quad (1) \\ -2x_{1} + 3x_{2} & = -4 \quad (2) \end{aligned} \]

We can represent the system in matrix form as: \[ A = \begin{bmatrix} 1 & -1 \\ -2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 1 \\ -4 \end{bmatrix} \]

Using matrix operations, we find the solution to the system: \[ \begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix} = \begin{bmatrix} -1 \\ -2 \end{bmatrix} \] Thus, we have: \[ x_{1} = -1, \quad x_{2} = -2 \]

Final Answer