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Interpret the Result 8=5 from Solving a System of Linear Equations
Mathematics
Grade 8 (Junior High School)
Question Content
You have solved a system of equations and your solution is: 8=5. Therefore:\n a) There is one solution\n b) There are infinitely many solutions\n c) The solution is 'all real numbers'\n d) There is no solution
Correct Answer
d
Detailed Solution Steps
1
Step 1: Analyze the resulting statement $8=5$. This is a false numerical statement with no variables remaining.
2
Step 2: Recall the rules for interpreting results of solving linear systems: A false statement with no variables means the two lines are parallel and never intersect.
3
Step 3: Match this result to the options: A false statement indicates there is no solution to the system, which corresponds to option d.
Knowledge Points Involved
1
Consistent and Inconsistent Linear Systems
A consistent system has at least one solution, while an inconsistent system has no solutions. When solving an inconsistent system, you will end up with a false numerical statement (like 8=5), which means the lines are parallel and never cross.
2
Solutions of Linear Systems
A system with one solution has two intersecting lines; a system with infinitely many solutions has two identical lines (resulting in a true statement like 0=0 when solved); a system with no solution has parallel, non-overlapping lines (resulting in a false statement).
3
Interpreting Algebraic Solution Results
When solving a system of equations, if you eliminate all variables and get a true statement, there are infinitely many solutions. If you get a false statement, there is no solution. If you solve for a specific variable value, there is exactly one solution.
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