Which conclusion is correct for the equations 6x − 5y = 17 and 18x − 15y = 51?
Answer and explanation
Correct answer: There are infinitely many solutions
Multiplying every term of 6x − 5y = 17 by 3 gives 18x − 15y = 51, which is the second equation. Hence the two equations are not independent; they are different algebraic forms of the same line. In ratio form, 18/6 = (−15)/(−5) = 51/17 = 3, confirming coincidence. A coincident pair has every point of the common line as a solution, so the number of solutions is infinite, not one or zero.
Frequently asked questions
What is the correct answer to this question?
There are infinitely many solutions
Why is this the correct answer?
Multiplying every term of 6x − 5y = 17 by 3 gives 18x − 15y = 51, which is the second equation. Hence the two equations are not independent; they are different algebraic forms of the same line. In ratio form, 18/6 = (−15)/(−5) = 51/17 = 3, confirming coincidence. A coincident pair has every point of the common line as a solution, so the number of solutions is infinite, not one or zero.
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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