What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
Answer and explanation
Correct answer: 231
For a pair of consistent and dependent linear equations, the corresponding coefficients and constant terms must have the same ratio. Here, 27=3×9 and 48=3×16, so the second equation must be three times the first. Therefore, s=3×77=231, making option C correct. Exam tip: In dependent equations, every corresponding term of one equation is obtained by multiplying the other equation by the same non-zero constant.
Frequently asked questions
What is the correct answer to this question?
231
Why is this the correct answer?
For a pair of consistent and dependent linear equations, the corresponding coefficients and constant terms must have the same ratio. Here, 27=3×9 and 48=3×16, so the second equation must be three times the first. Therefore, s=3×77=231, making option C correct. Exam tip: In dependent equations, every corresponding term of one equation is obtained by multiplying the other equation by the same non-zero constant.
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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