## Systems Ia.

Solve the following system of linear equations and verify the solution.

• #### Variant 1

$$\begin{array}{rcrcrcr} 3 x_1 &+& 2x_2 &+& x_3 &=\ & 5 \\ 2 x_1 &+& 3x_2 &+& x_3 &=\ & 1 \\ 2 x_1 &+& x_2 &+& 3x_3 &=\ & 11\\ 5 x_1 &+& 5x_2 &+& 2x_3 &=\ & 6 \end{array}$$

• #### Variant 2

$$\begin{array}{rcrcrcrcr} - x_1 &+& x_2 &+& 3x_3 & & &=\ & -2 \\ 2x_1 &-& x_2 &-& 6x_3 &+& x_4 &=\ & 2 \\ - x_1 &+& x_2 &+& 4x_3 & & &=\ & -2 \\ & & x_2 &+& 2x_3 &+& 2x_4 &=\ & 0 \end{array}$$

• #### Variant 3

$$\begin{array}{rcrcrcrcr} - x_1 &-& x_2 &+& 2 x_3 & & &=\ & 1 \\ 2 x_1 &+& 3x_2 &-& 4 x_3 &+& 3 x_4 &=\ & 1 \\ x_1 &+& x_2 &-& x_3 &+& 2 x_4 &=\ & 2 \\ &-& x_2 &+& 2 x_3 &+& 2 x_4 &=\ & 5 \\ \end{array}$$

• #### Variant 4

$$\begin{array}{rcrcrcrcr} 3 x_1 &-& x_2 &-& x_3 &-& 2x_4 &=\ & -4 \\ 2 x_1 &+& 3x_2 &+& 5x_3 &+& 2x_4 &=\ & -3 \\ 2 x_1 &+& 3x_2 &-& x_3 &-& x_4 &=\ & -6 \\ x_1 &+& x_2 &+& 2x_3 &+& 3x_4 &=\ & 1 \\ x_1 &+& 2x_2 &+& 3x_3 &-& x_4 &=\ & -4 \end{array}$$

• #### Variant 5

$$\begin{array}{rcrcrcrcrcr} 2 x_1 &+& 2 x_2 &+& 8 x_3 &-& 3 x_4 &+& 9 x_5 &=\ & 2 \\ 2 x_1 &+& 2 x_2 &+& 4 x_3 &-& x_4 &+& 3 x_5 &=\ & 2 \\ x_1 &+& x_2 &+& 3 x_3 &-& 2 x_4 &+& 3 x_5 &=\ & 1 \\ 3 x_1 &+& 3 x_2 &+& 5 x_3 &-& 2 x_4 &+& 3 x_5 &=\ & 1 \end{array}$$