What is s for infinitely many solutions of 12x + sy = 18 and 20x + 10y = 30?
Answer and explanation
Correct answer: s = 6
A pair of linear equations has infinitely many solutions when the ratios of the coefficients of x, the coefficients of y, and the constant terms are all equal. For the given equations, 12/20 = 3/5 and 18/30 = 3/5. Therefore, the middle ratio s/10 must also be 3/5. Hence s = 10 × 3/5 = 6. Option C is correct. If s were 4, 5, or 8, the y-coefficient ratio would differ from the other two ratios. The equations would then represent distinct intersecting or parallel lines rather than coincident lines, so they could not have infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
s = 6
Why is this the correct answer?
A pair of linear equations has infinitely many solutions when the ratios of the coefficients of x, the coefficients of y, and the constant terms are all equal. For the given equations, 12/20 = 3/5 and 18/30 = 3/5. Therefore, the middle ratio s/10 must also be 3/5. Hence s = 10 × 3/5 = 6. Option C is correct. If s were 4, 5, or 8, the y-coefficient ratio would differ from the other two ratios. The equations would then represent distinct intersecting or parallel lines rather than coincident lines, so they could not have infinitely many common solutions.
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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