Solve for the value of x in the system of equations:
$\begin{array}{l} 6 x + y - z = 4 \\ 2 x + 3 y + 5 z = 20 \\ - x + 2 y - 4 z = 6 \end{array}$

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Final Answer: The solution to the system of equations is $x = 0$ , $y = 5$ , and $z = 1$ . So, the value of $x$ is $0$ .

Steps

Step 1 ：We are given the system of equations: $6 x + y - z = 4$ , $2 x + 3 y + 5 z = 20$ , and $- x + 2 y - 4 z = 6$ .

Step 2 ：We can represent this system in matrix form as follows: $[\begin{matrix} 6 & 1 & - 1 \\ 2 & 3 & 5 \\ - 1 & 2 & - 4 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 4 \\ 20 \\ 6 \end{matrix}]$ .

Step 3 ：Solving this system of equations gives us the values of x, y, and z. However, the value of x is extremely close to zero, which is likely due to the precision of the floating point arithmetic. We can consider this value as zero for practical purposes.

Step 4 ：Final Answer: The solution to the system of equations is $x = 0$ , $y = 5$ , and $z = 1$ . So, the value of $x$ is $0$ .

Solve for the value of x in the system of equations: 6x+y−z=42x+3y+5z=20−x+2y−4z=6

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Solve for the value of x in the system of equations:
$\begin{array}{l} 6 x + y - z = 4 \\ 2 x + 3 y + 5 z = 20 \\ - x + 2 y - 4 z = 6 \end{array}$