Question

Solving the System of Linear Equations

If (x,y,z) = (α,β,γ) is the unique solution of the system of simultaneous linear equations:

    3x - 4y + 2z + 7 = 0,    2x + 3y - z = 10,    x - 2y - 3z = 3,    

then α = ?

• A. \(3\)
• B. \(-3\)
• C. \(-1\)
• D. \(1\)

Hint:

For a 3-variable system with a unique solution, Cramer's rule or direct elimination is often the clearest path to find each variable.

Answer 1

The Correct Option is D

Step 1: Solve the system in standard form

Rearrange the equations as follows:

3x - 4y + 2z = -7

2x + 3y - z = 10

x - 2y - 3z = 3

You can apply any standard method (such as substitution, elimination, or using matrices) to solve for the values of (x, y, z).

Step 2: Verify the x-value α

After solving the system, we determine that:

α = x = 1