Ise Gaussian elimination to find the complete solution to the system of equations, or show th \( \begin{array}{r}w+2 x+3 y-z=6 \\ 2 x-3 y+z=5 \\ w-4 x+y=3\end{array} \) A. There is one solution. The solution set is \( \{( \) the conrect choice below and fill in any answer boxes within your choice. B. There are infinitely many solutions. The solution set is \( \{\square\} \). (Simplify your answers.) Type expressions using \( z \) as the variable. Use integers or fractions for any numbers in C. There is no solution. The solution set is \( \varnothing \).

Solve the system of equations \( w+2x+3y-z=6;2x-3y+z=5;w-4x+y=3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}w+2x+3y-z=6\\2x-3y+z=5\\w-4x+y=3\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}w=6-2x-3y+z\\2x-3y+z=5\\w-4x+y=3\end{array}\right.\) - step2: Substitute the value of \(w:\) \(\left\{ \begin{array}{l}2x-3y+z=5\\6-2x-3y+z-4x+y=3\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}2x-3y+z=5\\6-6x-2y+z=3\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}z=5-2x+3y\\6-6x-2y+z=3\end{array}\right.\) - step5: Substitute the value of \(z:\) \(6-6x-2y+5-2x+3y=3\) - step6: Simplify: \(11-8x+y=3\) - step7: Move the expression to the right side: \(y=3-\left(11-8x\right)\) - step8: Subtract the terms: \(y=-8+8x\) - step9: Substitute the value of \(y:\) \(z=5-2x+3\left(-8+8x\right)\) - step10: Simplify: \(z=-19+22x\) - step11: Substitute the values of \(y,z:\) \(w=6-2x-3\left(-8+8x\right)-19+22x\) - step12: Simplify: \(w=11-4x\) - step13: Calculate: \(\left(w,x,y,z\right) = \left(11-4x,x,-8+8x,-19+22x\right),x \in \mathbb{R}\) - step14: Alternative Form: \(\textrm{Infinitely many solutions}\) The system of equations has infinitely many solutions. The solution set is \( \{\square\} \).