Which statement is correct for the pair 2x + 3y = 5 and 4x + 6y = 10?
Answer and explanation
Correct answer: There are infinitely many solutions
Multiplying 2x + 3y = 5 by 2 gives 4x + 6y = 10, exactly the second equation. Thus the two equations are equivalent and represent coincident lines. The ratio test confirms this: 4/2 = 6/3 = 10/5 = 2. Every point on the common line satisfies both equations, so the pair has infinitely many solutions. The value x = 0 is not the only possibility; for example, x = 1 gives y = 1, which satisfies both equations.
Frequently asked questions
What is the correct answer to this question?
There are infinitely many solutions
Why is this the correct answer?
Multiplying 2x + 3y = 5 by 2 gives 4x + 6y = 10, exactly the second equation. Thus the two equations are equivalent and represent coincident lines. The ratio test confirms this: 4/2 = 6/3 = 10/5 = 2. Every point on the common line satisfies both equations, so the pair has infinitely many solutions. The value x = 0 is not the only possibility; for example, x = 1 gives y = 1, which satisfies both equations.
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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