What is the relationship between the graphs represented by the equations \(2x+2y=18\) and \(x+y=9\)?
Answer and explanation
Correct answer: The same line
Dividing both sides of the first equation, \(2x+2y=18\), by \(2\) gives \(x+y=9\), which is exactly the second equation. Hence, both equations represent the same line and have infinitely many solutions. Exam tip: equations represent the same line when one is a non-zero multiple of the other.
Frequently asked questions
What is the correct answer to this question?
The same line
Why is this the correct answer?
Dividing both sides of the first equation, \(2x+2y=18\), by \(2\) gives \(x+y=9\), which is exactly the second equation. Hence, both equations represent the same line and have infinitely many solutions. Exam tip: equations represent the same line when one is a non-zero multiple of the other.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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