What should (s) be for the equations (6x+11y=53) and (18x+33y=s) to be consistent and dependent?
Answer and explanation
Correct answer: 159
For a pair of consistent and dependent linear equations, the ratios of the corresponding coefficients and constant terms must be equal. Here, \(18/6=33/11=3\), so \(s/53=3\), giving \(s=159\). If \(s\) were 158 or 160, the coefficients would still be in the ratio 3, but the constant terms would not be; the equations would then be inconsistent rather than dependent. Exam tip: In a dependent pair, one equation is an exact multiple of the other.
Frequently asked questions
What is the correct answer to this question?
159
Why is this the correct answer?
For a pair of consistent and dependent linear equations, the ratios of the corresponding coefficients and constant terms must be equal. Here, \(18/6=33/11=3\), so \(s/53=3\), giving \(s=159\). If \(s\) were 158 or 160, the coefficients would still be in the ratio 3, but the constant terms would not be; the equations would then be inconsistent rather than dependent. Exam tip: In a dependent pair, one equation is an exact multiple of the other.
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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