If (7x+4y=37) and (21x+12y=n) have infinitely many solutions then what is (n)?
Answer and explanation
Correct answer: 111
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constant terms must be equal. Here, the coefficients of x and y in the second equation are three times those in the first: 21=3×7 and 12=3×4. Therefore, the constant term must also be three times 37, so n=3×37=111. Hence, option C is correct. Exam tip: Infinitely many solutions mean that both equations represent the same line.
Frequently asked questions
What is the correct answer to this question?
111
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constant terms must be equal. Here, the coefficients of x and y in the second equation are three times those in the first: 21=3×7 and 12=3×4. Therefore, the constant term must also be three times 37, so n=3×37=111. Hence, option C is correct. Exam tip: Infinitely many solutions mean that both equations represent the same line.
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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