Question

The system of equations 2x + 1 = 0 and 8y − 5 = 0 has ______.

Options

• unique solution

• two solutions

• no solution

• infinite number of solutions

Answer 1

The system of equations 2x + 1 = 0 and 8y − 5 = 0 has unique solution.

Explanation:

To determine the number of solutions for the given system of equations: 

2x + 1 = 0 

3y − 5 = 0

Rewriting them:

2x = −1

 => ` x = -1/2`

3y = 5

=> `y = 5/3`

• These equations represent two lines: one is a vertical line (`x = -1/2`) and the other is a horizontal line (`y = 5/3`).
• A vertical line and a horizontal line always intersect at a single point.
• That means the system has a unique solution.