Questions: Solve the given system of equations. x+y+9z=-37 x+y+5z=-21 x-8y+2z=36

Solution Steps

To solve the given system of equations, we can use matrix operations. We will represent the system as a matrix equation \(AX = B\), where \(A\) is the coefficient matrix, \(X\) is the column matrix of variables, and \(B\) is the column matrix of constants. We can then use a numerical method, such as NumPy's linear algebra solver, to find the values of \(x\), \(y\), and \(z\).

We start with the system of equations given by: \[ \begin{align*}

1. & \quad x + y + 9z = -37 \\
2. & \quad x + y + 5z = -21 \\
3. & \quad x - 8y + 2z = 36 \end{align*} \]

By applying methods for solving linear equations, we find the values of the variables \(x\), \(y\), and \(z\). The solution yields: \[ \begin{align_} x & = 4 \\ y & = -5 \\ z & = -4 \end{align_} \]

Final Answer