What type of pair is formed by the equations (20x+28y=84) and (5x+7y=23)?
Answer and explanation
Correct answer: Inconsistent (parallel lines)
The ratios of the first two coefficients are equal: \(\frac{20}{5}=\frac{28}{7}=4\). However, the ratio of the constants, \(\frac{84}{23}\), is not equal to 4. Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), so the lines are parallel and have no common solution. Hence, the pair is inconsistent. Exam tip: Compare all three ratios to identify the consistency of a pair quickly.
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What is the correct answer to this question?
Inconsistent (parallel lines)
Why is this the correct answer?
The ratios of the first two coefficients are equal: \(\frac{20}{5}=\frac{28}{7}=4\). However, the ratio of the constants, \(\frac{84}{23}\), is not equal to 4. Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), so the lines are parallel and have no common solution. Hence, the pair is inconsistent. Exam tip: Compare all three ratios to identify the consistency of a pair quickly.
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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