What type of pair is formed by the equations (22x+33y=99) and (2x+3y=11)?
Answer and explanation
Correct answer: Inconsistent
Compare the corresponding coefficients: \(\frac{22}{2}=11\) and \(\frac{33}{3}=11\), but \(\frac{99}{11}=9\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), which is the condition for an inconsistent pair. The two lines are distinct and parallel, so the equations have no solution. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\); the pair is dependent only when all three ratios are equal.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
Compare the corresponding coefficients: \(\frac{22}{2}=11\) and \(\frac{33}{3}=11\), but \(\frac{99}{11}=9\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), which is the condition for an inconsistent pair. The two lines are distinct and parallel, so the equations have no solution. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\); the pair is dependent only when all three ratios are equal.
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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