Final answer:
After testing all options provided for the system of equations, none of the choices satisfy all three equations. Therefore, none of the given options are correct solutions to the system.
Step-by-step explanation:
To solve the system of equations for x, y, and z, we can apply methods such as substitution, elimination, or matrix operations. However, since we're given multiple choice answers, we can simply check each option by substituting the values into the original equations to verify the solution.
Testing Option 1: x = 2, y = -1, z = -4.
First equation: 7(2) + 23(-1) + (-4) = 14 - 23 - 4 = -13 ≠ 20,
Second equation: 3(2) + 10(-1) + 4(-4) = 6 - 10 - 16 = -20 ≠ -6,
Third equation: (2) + 3(-1) - 2(-4) = 2 - 3 + 8 = 7 ≠ 9.
This option is incorrect; the values do not satisfy all equations.
Testing Option 2: x = 1, y = -2, z = 3.
First equation: 7(1) + 23(-2) + 3 = 7 - 46 + 3 = -36 ≠ 20,
Second equation: 3(1) + 10(-2) + 4(3) = 3 - 20 + 12 = -5 ≠ -6,
Third equation: (1) + 3(-2) - 2(3) = 1 - 6 - 6 = -11 ≠ 9.
This option is incorrect; the values do not satisfy all equations.
Testing Option 3: x = -3, y = 5, z = -2.
First equation: 7(-3) + 23(5) + (-2) = -21 + 115 - 2 = 92 ≠ 20,
Second equation: 3(-3) + 10(5) + 4(-2) = -9 + 50 - 8 = 33 ≠ -6,
Third equation: (-3) + 3(5) - 2(-2) = -3 + 15 + 4 = 16 ≠ 9.
This option is also incorrect; the values do not satisfy all equations.
Testing Option 4: x = 4, y = 0, z = -3.
First equation: 7(4) + 23(0) + (-3) = 28 + 0 - 3 = 25 ≠ 20,
Second equation: 3(4) + 10(0) + 4(-3) = 12 + 0 - 12 = 0 ≠ -6,
Third equation: (4) + 3(0) - 2(-3) = 4 + 0 + 6 = 10 ≠ 9.
This option is also incorrect; the values do not satisfy all equations.
It seems there might be a mistake as none of the provided options are the correct solution to the system of equations given.