Questions: Determine if the given ordered triple is a solution of the system. (-1,5,1) x+y+z=5 x-y+5z=-1 2x+y+z=4 solution not a solution

Solution Steps

To determine if the ordered triple \((-1, 5, 1)\) is a solution to the system of equations, substitute \(x = -1\), \(y = 5\), and \(z = 1\) into each equation. Check if all equations are satisfied with these values.

We substitute the ordered triple \((-1, 5, 1)\) into the equations of the system:

1. For the first equation \(x + y + z = 5\): \[ -1 + 5 + 1 = 5 \quad \text{(True)} \]

2. For the second equation \(x - y + 5z = -1\): \[ -1 - 5 + 5 \cdot 1 = -1 \quad \text{(True)} \]

3. For the third equation \(2x + y + z = 4\): \[ 2 \cdot (-1) + 5 + 1 = 4 \quad \text{(True)} \]

All three equations are satisfied:

• \(eq1 = \text{True}\)
• \(eq2 = \text{True}\)
• \(eq3 = \text{True}\)

Since all equations are satisfied, the ordered triple \((-1, 5, 1)\) is indeed a solution to the system of equations.

Final Answer