Question

The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:

• A. consistent with unique solution
• B. inconsistent
• C. consistent with infinitely many solutions
• D. None of the above

Hint:

A system of linear equations is consistent and has a unique solution if the determinant of the coefficient matrix is non-zero.

Answer 1

The Correct Option is A

Solving the system of equations, we find that there exists a unique solution for \( x \) and \( y \), making the system consistent with a unique solution.

Step 2: Conclusion.
Thus, the correct answer is (1).