What is the most suitable conclusion by observing the equations (8x+15y=73) and (24x+45y=219)?
Answer and explanation
Correct answer: There are infinitely many solutions
The second equation is exactly 3 times the first: multiplying 8x+15y=73 by 3 gives 24x+45y=219. Hence, both equations represent the same line, so the system has infinitely many solutions. Exam tip: if \(a_1/a_2=b_1/b_2=c_1/c_2\), the lines are coincident and infinitely many solutions exist.
Frequently asked questions
What is the correct answer to this question?
There are infinitely many solutions
Why is this the correct answer?
The second equation is exactly 3 times the first: multiplying 8x+15y=73 by 3 gives 24x+45y=219. Hence, both equations represent the same line, so the system has infinitely many solutions. Exam tip: if \(a_1/a_2=b_1/b_2=c_1/c_2\), the lines are coincident and infinitely many solutions exist.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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