For each of the following systems of equations, determine whether or not it has a solution. If so, calculate all possible solutions: a) x + y + z = 1; 2x - y + 2z = - 1 b) x + y + z = 1; 2x - y + 2z = - 1; x + y - z = 2

a.) has no solution b.) Add equation 2 and 3 (2x-y+2z=-1) + (x+y-z=2), the resulting equation will be 2x+2y=3 -2(equation 1) + equation 2, -2(x+y+z=1) + (2x-y+2z=-1), the resulting equation will be (-2x-2y-2z=-2) + (2x-y+2z=-1) -3y = -3 y=1 2x+2y=3 2x+2(1)=3 2x+2=3 2x=1 x=1/2 x+y+z=1 1/2 + 1 + z = 1 z=1-1-1/2 z=-1/2 has a solution: x=1/2, y=1, z=-1/2