Question

The system of equations \(x+5=0\) and \(2x-1=0\) has

• A. No solution
• B. Unique solution
• C. Two solutions
• D. Infinite solutions

Hint:

If two linear equations in one variable yield different values, the system is inconsistent.

Answer 1

The Correct Option is A

Given system of equations:
\[ x + 5 = 0 \] \[ 2x - 1 = 0 \]

Step 1: Solve each equation separately
From first equation:
\[ x = -5 \]
From second equation:
\[ 2x = 1 \implies x = \frac{1}{2} \]

Step 2: Compare solutions
First equation gives \(x = -5\), second gives \(x = \frac{1}{2}\).
Since \(x\) cannot be both values simultaneously, the system has no common solution.

Final Answer:
\[ \boxed{\text{No solution}} \]