Solve the given system of equations x y z 1 1 3x 3y z

Solve the given system of equations. {x - y - z = 1 (1) 3x + 3y + z = 1 (2) 16x + 8y = 0 (3) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. There is one solution. The solution is (Simplify your answer.) There are infinitely many solutions. The solution set is {(x, y, z) | x =, y =, z any real number)}. (Simplify your answer.) There is no solution. There are infinitely many solutions. The solution set is {(x, y, z) | x =, y any real number, z any real number)}. (Simplify your answer.)

Solution

x -y -z = 1 ---(1)

3x +3y + z = 1 ----(2)

16x +8y =0 ----> 2x +y =0 ----(3)

y = -2x

So, pluggin y = -2x in equation 1 and 2:

x + 2x -z =1 ----> 3x - z =1

3x +-6x +z =1 ----> -3x +z = 1

Add the two reduced equations we get 0 = 2

This is inconsistent . No solution