What is the relationship between the lines represented by the equations \(3x+3y=24\) and \(x+y=8\)?
Answer and explanation
Correct answer: The same line
Dividing every term of the first equation, \(3x+3y=24\), by 3 gives \(x+y=8\), which is the second equation. Hence, both equations represent the same line and have infinitely many common solutions. Exam tip: If one linear equation is a non-zero constant multiple of the other, their graphs are coincident, or the same line.
Frequently asked questions
What is the correct answer to this question?
The same line
Why is this the correct answer?
Dividing every term of the first equation, \(3x+3y=24\), by 3 gives \(x+y=8\), which is the second equation. Hence, both equations represent the same line and have infinitely many common solutions. Exam tip: If one linear equation is a non-zero constant multiple of the other, their graphs are coincident, or the same line.
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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