Question

The system of equations \(x = 2\) and \(x = 3\) has:

• A. unique solution (2, 3)
• B. two solutions (2, 0) and (3, 0)
• C. no solution
• D. infinitely many solutions

Hint:

Graphically, the solution is the point of intersection. Since a single point cannot have an x-value of both 2 and 3 at the same time, it's impossible for these lines to meet.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A system of linear equations has a solution only if the lines intersect at one or more points. In a 2D plane, the equation \(x = c\) represents a vertical line passing through the value \(c\) on the x-axis.
Step 2: Key Formula or Approach:
Parallel lines never intersect. If the lines are parallel and not coincident, the system has no solution.
Step 3: Detailed Explanation:
1. The equation \(x = 2\) is a vertical line where every point has an x-coordinate of 2.
2. The equation \(x = 3\) is a vertical line where every point has an x-coordinate of 3.
3. These two lines are parallel to each other and to the y-axis.
4. Since they never intersect, there is no point \((x, y)\) that can satisfy both equations simultaneously.
Step 4: Final Answer:
The system has no solution.