Question

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.

Answer 1

-2x+2y+2z=4 (a)

-5x+2y-3z=-4 (b)

8x-2y+8z =13 (c)

Add and subtract two equations to eliminate 1 variable:

Add b and c:

-5x+2y-3z=-4 (b)

+

8x-2y+8z =13 (c)

________________

3x+5z= 9 (1)

Subtract (b) to (a)

-2x+2y+2z=4 (a)

-

-5x+2y-3z=-4 (b)

_____________

3x +5z =8 (2)

Now we have a system of 2 equations: (1) and (2)

3x+5z= 9 (1)

3x +5z =8 (2)

Subtract (2) to (1)

0 = 1

0 is not equal to one so there is no solutions.

Correct option:

NO solutions; inconsistent