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

Step 1: Solve equation 1
\( 2x + 1 = 0 \Rightarrow 2x = -1 \Rightarrow x = -\frac{1}{2}\)
Step 2: Solve equation 2
\( 3y - 5 = 0 \Rightarrow 3y = 5 \Rightarrow y = \frac{5}{3}\)
Step 3: Solution Type
The equations provide direct and independent values for \(x\) and \(y\), thus the system has one solution:
\[x = -\frac{1}{2},\quad y = \frac{5}{3}\]
Final Answer:
The system has a unique solution.