SOLUTION: Solve the system of equation x+y+z=9, -x+y+z=1, and x-y-z=5 A. There is no solution. B. There are infinitely many solutions. C. There is one solution, x=4, y=2, and z=3. D.

Question 1127839: Solve the system of equation x+y+z=9, -x+y+z=1, and x-y-z=5
A. There is no solution.
B. There are infinitely many solutions.
C. There is one solution, x=4, y=2, and z=3.
D. There is not enough information to solve the problem
Found 3 solutions by htmentor, MathTherapy, ikleyn:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
Solving eq. 2 for x, we have x = y + z - 1
Substitute into eq. 3:
y + z - 1 - y - z = 5
y and z cancels out and we are left with:
-1 = 5
This is obviously not true, so there are no solutions
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Solve the system of equation x+y+z=9, -x+y+z=1, and x-y-z=5
A. There is no solution.
B. There are infinitely many solutions.
C. There is one solution, x=4, y=2, and z=3.
D. There is not enough information to solve the problem

x + y + z = 9 ----- eq (i)
- x + y + z = 1 ----- eq (ii)
x - y - z = 5 ----- eq (iii)
All you have to do here is ADD eqs (ii) & (iii). All 3 variables will be ZEROED out on the left, leaving the equation: 0 = 6.
Obviously, this is FALSE so no solutions exist ().
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
You can easily solve the problem and answer the question MENTALLY, without writing any equations.

Simply notice that the second and the third equations have their left sides with opposite signs;
but the right sides are not the opposite numbers.

Hence, the system HAS NO solution.

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