What should (s) be for (4x+5y=29) and (8x+10y=s) to be consistent and dependent?
Answer and explanation
Correct answer: 58
For a pair of linear equations to be consistent and dependent, all corresponding coefficients and constants must be proportional. The coefficients in the second equation are twice those in the first: \(8=2\times4\) and \(10=2\times5\). Therefore, the constant must also be doubled, so \(s=2\times29=58\). Hence, option C is correct. Values such as 56 or 57 would not make the two equations represent the same line. Exam tip: for dependent equations, check whether \(a_1/a_2=b_1/b_2=c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
58
Why is this the correct answer?
For a pair of linear equations to be consistent and dependent, all corresponding coefficients and constants must be proportional. The coefficients in the second equation are twice those in the first: \(8=2\times4\) and \(10=2\times5\). Therefore, the constant must also be doubled, so \(s=2\times29=58\). Hence, option C is correct. Values such as 56 or 57 would not make the two equations represent the same line. Exam tip: for dependent equations, check whether \(a_1/a_2=b_1/b_2=c_1/c_2\).
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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