How will the lines \(3x+6y=24\) and \(x+2y=8\) appear on the graph?
Answer and explanation
Correct answer: Coincident
Dividing every term of the first equation by 3 gives \(x+2y=8\), which is exactly the second equation. Hence both equations represent the same line on the graph, so the lines are coincident and have infinitely many solutions. Parallel distinct lines require the constant terms not to be in the same ratio as the coefficients. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\); if all three ratios are equal, the lines are coincident.
Frequently asked questions
What is the correct answer to this question?
Coincident
Why is this the correct answer?
Dividing every term of the first equation by 3 gives \(x+2y=8\), which is exactly the second equation. Hence both equations represent the same line on the graph, so the lines are coincident and have infinitely many solutions. Parallel distinct lines require the constant terms not to be in the same ratio as the coefficients. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\); if all three ratios are equal, the lines are coincident.
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..
