Question

Solve the given system of equations. If the system has no solution, say that it is inconsistent x - 2y + 3z 6 2x + y + z = - 3 - 3x + 2y - 22 = -3 Select the correct choice below and fill in any answer boxes within your choice. y .z any real number) A. The solution is x-..y- and z= (Type integers or simplified fractions.) OB. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(xy.z) x= (Simplify your answers. Type expressions using z as the variable as needed.) OC. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(x.y.z) = (Simplify your answer. Type an expression using y and as the variables as needed.) OD. The system is inconsistent .y any real number, z any real number)

Answer 1

1 2 -3 -2 1 2 3 1 -2 6 -3 -3 Operate R +3R, → R, R, - 2R, ™R 11 -2 3 61 So, 0 5 -5 -15 0 -4 7 15 Operate R*R So, 1 -2 0 1 0 -4 3 -1 7 6 -3 15 Operate R +2R, → RR +4R, ™R So, 1 0 1 0 1 -1 0 0 3 0 -3 3 Operate R, ™R So, 1 0 0 0 1 0 1 -1 1 0 -3 1 Operate R- R R R+R → R, So, 1 00 -1 0 1 0 -2 0 0 1 1 This is in RREF. So, x=-1, y=-2,2 = 1 So, the solution is x=-1, y=-2,2=1. So, option (A) is the correct chice.