An infeasible linear system

The system of equations in unknowns

$begin{array}{rcl} 3 x_1 + 4.5 x_2 &=& 1, 2x_1 + 1.2 x_2 &=& -3.2, -0.1 x_1 + 8.2 x_2 &=& 1.5, end{array}$

can be written as Ax = y , where is the 3 times 2 matrix

A = left( begin{array}{cc} 3 & 4.5 2 & 1.2 -0.1 & 8.2 end{array}right) ,

and is the -vector

y = left( begin{array}{c} 1 -3.2 1.5 end{array}right) .

The set of solutions turns out to be empty. Indeed, if we use the first two equations, and solve for x_1,x_2 , we get x = (-2.8889, 2.1481) , but then the last equation is not satisfied, since -0.1 x_1 + 8.2 x_2 = 17.4741 ne 1.5 .