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:
- What is the condition for two lines to be parallel in terms of their slopes?
- How do you identify parallel lines from their equations?
- What happens if two lines coincide instead of being just parallel?
- How can parallelism of lines be visualized in three dimensions?
- 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 +
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Do Parallel Lines Cross? Understanding the Relationship Between Parallel Lines and Slope
Understanding Parallel Lines in Systems of Equations
Identifying Properties of Parallel Lines in Coordinate Geometry
Identifying Parallel Lines in Systems of Equations: Contradiction Example
Identifying Parallel Lines in a System of Equations: Analyzing Contradictions like 3 = 2