Solve the system x1 x2 2x35 5x1 4x2 7x36 3x1 3x342 x1 x2 x3

Solve the system {x1 -x2 -2x3=-5 5x1 -4x_2 -7x3=-6 -3x_1 -3x_3=-42 [x_1 x_2 x_3]

Solution

Clearly x₂ =x₄ (from the first and the last equations)

So the general solution to the system (it has infinitely many solutions) is

                   x₁ = -4-x₂

                   x₃ = -3-x₂

                  x₄ = x₂

(x₂ any arbitrary real number)