Using Gaussian elimination: x + y + z = 9 / * ( - 2 ) / ( - 1 ) ( we will multiply by - 2 and add to the 2nd 2 x - 3 y + 4 z = 7 equation and multiply by - 1 and add to the 3rd equation ) x - 4 y + 3 z = - 2 ----------------------------- x + y + z = 9 - 5 y + 2 z = - 11 / * ( - 1 ) - 5 y + 2 z = - 11 --------------------------- x + y + z = 9 - 5 y + 2 z = - 11 0 z = 0 There are infinitely many solutions to the system of equations. z = t, - 5 y + 2 t = - 11 5 y = 11 + 2 t y = ( 11 + 2 t ) / 2 x + ( 11 + 2 t ) / 2 + t = 9 / * 2 2 x + 11 + 2 t + 2 t = 18 2 x = 18 - 11 - 4 t x = ( 7 - 4 t ) / 2 ( x, y , z ) = ( (7 - 4 t ) / 2, ( 11 + 2 t ) / 2, t )
