Math Problem Statement

If two lines are parallel, then what is the nature of its solution?

There is no solution.

There is a unique solution.

There are infinite number of solutions.

All of the choices.

Solution

If two lines are parallel, they never intersect. Therefore, the system of equations representing these lines has no solution.

The correct answer is:

There is no solution.

Would you like details or have any questions? Here are five related questions to expand your understanding:

  1. What is the condition for two lines to be parallel in terms of their slopes?
  2. How do you identify parallel lines from their equations?
  3. What happens if two lines coincide instead of being just parallel?
  4. How can parallelism of lines be visualized in three dimensions?
  5. How do parallel lines behave in different coordinate systems, such as polar coordinates?

Tip: Parallel lines have the same slope in their slope-intercept form ( y = mx +

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Parallel Lines
Systems of Equations

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Equations of parallel lines have equal slopes

Theorems

Parallel Line Theorem
Properties of Linear Systems

Suitable Grade Level

Grades 8-10