Use the Cramer\'s rule to solve the system of equations. If D=0, use another met

Question

Use the Cramer's rule to solve the system of equations. If D=0, use another method to determine the solution set.

4x - 8y + z + 8 = 0 -2x + 3y + 5z + 40 =0 8x - 2y - z - 8 = 0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. There is one solution. The solution set is { }. (Simplify your answers.) There are infinitely many solutions. The solution set is { , z} where z is any real number. (Simplify your answers. Type expressions using z as the variable.) There is no solution. The solution set is

Explanation / Answer

4 -8 1

-2 3 5

8 -2 -1

D = 4(-3 +10) + 8(2 - 40) + 1 (4 - 24) = -296

x = D1/D = 0 / -296 = 0

y = D2 / D = 0/-296 = 0

z = D3 / D = 2368 / -296 = -8

So, solution set by solving is (x,y,z) = (0,0,-8)

So, the correct option is A.

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