The system of equations x + 3y + 7 = 0, 3x + | vedclass

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(C) To determine the nature of the solutions, we first write the system in the form $AX = B$ or evaluate the determinant of the coefficient matrix $\D

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(C) To determine the nature of the solutions, we first write the system in the form $AX = B$ or evaluate the determinant of the coefficient matrix $\Delta$.The system is:$1x + 3y + 0z = -7$$3x + 10y - 3z = -18$$0x + 3y - 9z = -2$The determinant of the coefficient matrix $\Delta$ is:$\Delta = \begin{vmatrix} 1 & 3 & 0 \ 3 & 10 & -3 \ 0 & 3 & -9 \end{vmatrix} = 1(10(-9) - (-3)(3)) - 3(3(-9) - 0) + 0 = 1(-90 + 9) - 3(-27) = -81 + 81 = 0$.Since $\Delta = 0$, the system either has no solution or infinitely many solutions.Now, we calculate $\Delta_1$ (replacing the first column with the constants):$\Delta_1 = \begin{vmatrix} -7 & 3 & 0 \ -18 & 10 & -3 \ -2 & 3 & -9 \end{vmatrix} = -7(-90 + 9) - 3(162 - 6) + 0 = -7(-81) - 3(156) = 567 - 468 = 99$.Since $\Delta = 0$ and $\Delta_1 
eq 0$, the system of equations is inconsistent and has no solution.

The system of equations $x + 3y + 7 = 0$, $3x + 10y - 3z + 18 = 0$ and $3y - 9z + 2 = 0$ has

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