Question

The system of linear equations \( 2x - 3y = 5 \) and \( 4x - 6y = 7 \) has:

• A. One and only one solution
• B. No solution
• C. Infinitely many solutions
• D. None of these

Hint:

If two equations are multiples of each other but have different constants, the system has no solution.

Answer 1

The Correct Option is B

We are given the system of equations: 1) \( 2x - 3y = 5 \) 2) \( 4x - 6y = 7 \) Notice that the second equation is exactly double the first equation: \[ 4x - 6y = 7 \quad \Rightarrow \quad 2(2x - 3y) = 7. \] Thus, the system is inconsistent, as the first equation gives 10 when multiplied by 2, but the second equation gives 7. Therefore, the system has no solution. Thus, the correct answer is \( \boxed{\text{No solution}} \).