Question

The system of equations $2x + 1 = 0$ and $3y - 5 = 0$ has

• A. unique solution
• B. two solutions
• C. no solution
• D. infinite number of solutions

Hint:

Two independent linear equations in two variables intersect at one point.

Answer 1

The Correct Option is A

Given:
The system of equations:
1) \( 2x + 1 = 0 \)
2) \( 3y - 5 = 0 \)

Step 1: Solve the first equation
\[ 2x + 1 = 0 \Rightarrow 2x = -1 \Rightarrow x = -\frac{1}{2} \]
Step 2: Solve the second equation
\[ 3y - 5 = 0 \Rightarrow 3y = 5 \Rightarrow y = \frac{5}{3} \]
Step 3: Nature of the system
Since both equations give direct and independent values of \(x\) and \(y\), the system has exactly one solution:
\[ x = -\frac{1}{2},\quad y = \frac{5}{3} \]
Final Answer:
The system has a unique solution.