Question

X - y - 2z = 4 -x 3y - z = 8 -2x - y - 4z = -1 given that (3, 3, –2) is a solution to the given system, the point is solution(s) to the system shown.

Answer 1

The point (3, 3, -2) satisfies all three given equations when substituted in, confirming it as a solution to the system of linear equations.

Step-by-step explanation:

The question is asking to verify if the point (3, 3, -2) is a solution to the given system of linear equations:

• X - y - 2z = 4
• -x + 3y - z = 8
• -2x - y - 4z = -1

To determine if (3, 3, -2) is a solution, we substitute x = 3, y = 3, and z = -2 into each of the three equations and see if the equations hold true.

1. Substituting into the first equation: 3 - 3 - 2(-2) = 3 - 3 + 4 = 4, which is true.
2. Substituting into the second equation: -3 + 3(3) - (-2) = -3 + 9 + 2 = 8, which is also true.
3. Substituting into the third equation: -2(3) - 3 - 4(-2) = -6 - 3 + 8 = -1, which is true as well.

Since all three equations are satisfied, the point (3, 3, -2) is indeed a solution to the system of equations.