a11*x1+a12*x2+a13*x3=b1 a ... 2 a31*x1+a32*x2+a33*x3=b3
Решение
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a11*x1 + a12*x2 + a13*x3 = b1
$$a_{13} x_{3} + \left(a_{11} x_{1} + a_{12} x_{2}\right) = b_{1}$$
a21*x1 + a22*x2 + a23*x3 = b2
$$a_{23} x_{3} + \left(a_{21} x_{1} + a_{22} x_{2}\right) = b_{2}$$
a31*x1 + a32*x2 + a33*x3 = b3
$$a_{33} x_{3} + \left(a_{31} x_{1} + a_{32} x_{2}\right) = b_{3}$$
или
$$\begin{cases}a_{13} x_{3} + \left(a_{11} x_{1} + a_{12} x_{2}\right) = b_{1}\\a_{23} x_{3} + \left(a_{21} x_{1} + a_{22} x_{2}\right) = b_{2}\\a_{33} x_{3} + \left(a_{31} x_{1} + a_{32} x_{2}\right) = b_{3}\end{cases}$$
Быстрый ответ
$$a_{11 1} = - \frac{a_{12} x_{2} + a_{13} x_{3} - b_{1}}{x_{1}}$$
=
$$\frac{- a_{12} x_{2} - a_{13} x_{3} + b_{1}}{x_{1}}$$
=
$$a_{21 1} = - \frac{a_{22} x_{2} + a_{23} x_{3} - b_{2}}{x_{1}}$$
=
$$\frac{- a_{22} x_{2} - a_{23} x_{3} + b_{2}}{x_{1}}$$
=
$$a_{31 1} = - \frac{a_{32} x_{2} + a_{33} x_{3} - b_{3}}{x_{1}}$$
=
$$\frac{- a_{32} x_{2} - a_{33} x_{3} + b_{3}}{x_{1}}$$
=
=
$$\frac{- a_{12} x_{2} - a_{13} x_{3} + b_{1}}{x_{1}}$$
=
-(-b1 + a12*x2 + a13*x3)/x1
$$a_{21 1} = - \frac{a_{22} x_{2} + a_{23} x_{3} - b_{2}}{x_{1}}$$
=
$$\frac{- a_{22} x_{2} - a_{23} x_{3} + b_{2}}{x_{1}}$$
=
-(-b2 + a22*x2 + a23*x3)/x1
$$a_{31 1} = - \frac{a_{32} x_{2} + a_{33} x_{3} - b_{3}}{x_{1}}$$
=
$$\frac{- a_{32} x_{2} - a_{33} x_{3} + b_{3}}{x_{1}}$$
=
-(-b3 + a32*x2 + a33*x3)/x1