Question

X - y - 2z &= 4

-x + 3y - z &= 8
-2x - y - 4z &= -1
If (3, 3, –2) is a solution to the system, the point is solution(s) to the system shown.
a) Yes
b) No

Answer 1

Substituting the given point into each equation of the system and comparing the left and right sides to determine if the point is a solution. Hence, the answer is No.

Step-by-step explanation:

In order to determine whether the point (3, 3, -2) is a solution to the given system of equations, we substitute the values of x, y, and z into each equation and check if the left side of the equation is equal to the right side. Substituting (3, 3, -2) into the first equation, we have: x - y - 2z = 3 - 3 - 2(-2) = 3 + 3 + 4 = 10.

Since 10 is not equal to 4, the first equation is not satisfied. Similarly, substituting (3, 3, -2) into the second equation:
-x + 3y - z = -3 + 9 + 2 = 8. Since 8 is equal to 8, the second equation is satisfied. Finally, substituting (3, 3, -2) into the third equation: -2x - y - 4z = -6 - 3 - 8 = -17.

Since -17 is not equal to -1, the third equation is not satisfied. Therefore, (3, 3, -2) is not a solution to the system of equations.