Math Problem Statement
Solution
The image contains a system of linear equations:
Let's solve this system to find the point of intersection, if it exists.
Step 1: Analyze the system
Both equations appear to have the same left-hand side but different right-hand sides:
Step 2: Subtract one equation from the other
Subtract Equation 1 from Equation 2 to eliminate and :
Step 3: Interpretation
The result is a contradiction, which indicates that there is no solution. This system of equations is inconsistent, meaning the lines are parallel and do not intersect.
Conclusion
The system of equations does not have a point of intersection. The two lines represented by these equations are parallel.
Would you like more details on this solution or have any other questions?
Here are 5 related questions you might find interesting:
- How can we tell if two lines are parallel from their equations?
- What are the possible outcomes when solving a system of linear equations?
- How do we find the point of intersection for consistent systems of equations?
- What methods can be used to solve a system of equations besides substitution and elimination?
- How can we graphically represent parallel lines?
Tip: When two equations in a system have the same coefficients for all variables but different constants, the system is inconsistent, leading to parallel lines with no intersection.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Parallel Lines
Formulas
Standard form of a linear equation: Ax + By = C
Theorems
If two linear equations have the same coefficients for variables but different constants, the lines are parallel.
Suitable Grade Level
Grades 8-10
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