What type of pair is formed by the equations (18x+27y=63) and (2x+3y=8)?
Answer and explanation
Correct answer: Inconsistent
For the first equation, \(a_1=18, b_1=27, c_1=63\), and for the second, \(a_2=2, b_2=3, c_2=8\). Here, \(a_1/a_2=18/2=9\) and \(b_1/b_2=27/3=9\), but \(c_1/c_2=63/8\), which is not 9. Thus, the two lines are distinct and parallel, so they have no common solution. Therefore, the pair is inconsistent. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair is inconsistent.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
For the first equation, \(a_1=18, b_1=27, c_1=63\), and for the second, \(a_2=2, b_2=3, c_2=8\). Here, \(a_1/a_2=18/2=9\) and \(b_1/b_2=27/3=9\), but \(c_1/c_2=63/8\), which is not 9. Thus, the two lines are distinct and parallel, so they have no common solution. Therefore, the pair is inconsistent. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair is inconsistent.
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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