What type of pair is formed by 11x + 7y = 30 and 4x + 3y = 12?
Answer and explanation
Correct answer: Consistent and independent
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, a unique solution occurs when a₁/a₂ ≠ b₁/b₂. Here the ratios of the x- and y-coefficients are 11/4 and 7/3. They are unequal because 11 × 3 = 33, whereas 7 × 4 = 28. Hence the corresponding lines have different slopes and intersect at exactly one point. A pair with one common solution is called consistent and independent. It is not dependent, because dependent equations represent the same line and require all three coefficient ratios to be equal. It is not inconsistent or parallel, because those descriptions apply when the lines have the same slope but are distinct. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
Consistent and independent
Why is this the correct answer?
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, a unique solution occurs when a₁/a₂ ≠ b₁/b₂. Here the ratios of the x- and y-coefficients are 11/4 and 7/3. They are unequal because 11 × 3 = 33, whereas 7 × 4 = 28. Hence the corresponding lines have different slopes and intersect at exactly one point. A pair with one common solution is called consistent and independent. It is not dependent, because dependent equations represent the same line and require all three coefficient ratios to be equal. It is not inconsistent or parallel, because those descriptions apply when the lines have the same slope but are distinct. Therefore option C is correct.
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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