Math  /  Algebra

QuestionUse Gaussian elimination to find the complete solution to the system of equations, or show that none exists. {2x+3y+4z=202x4y6z=16x+yz=4\left\{\begin{array}{rr} 2 x+3 y+4 z= & -20 \\ 2 x-4 y-6 z= & 16 \\ x+y-z= & 4 \end{array}\right.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution set is {(,,)}\{(\square, \square, \square)\}. \square (Simplify your answers.) B. There are infinitely many solutions. The solution set is {(,,z)}\{(\square, \square, z)\}, where zz is any real number. \square \square (Type expressions using zz as the variable. Use integers or fractions for any numbers in the expressions.) C. There is no solution. The solution set is \varnothing.

Studdy Solution
So, our solution is x=3x = \mathbf{-3}, y=2y = \mathbf{2}, and z=5z = \mathbf{-5}.
This means there is one solution, and the solution set is {(3,2,5)}\{(\mathbf{-3}, \mathbf{2}, \mathbf{-5})\}.
We should choose option A!

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