What type of pair is (18x+27y=63) and (2x+3y=8)?
Answer and explanation
Correct answer: Parallel but distinct lines; inconsistent
The coefficients of the first equation are 9 times those of the second: \(18/2=27/3=9\). However, the ratio of the constants is \(63/8\), which is not 9. Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are parallel but distinct and the pair is inconsistent; it has no solution. For coincident lines, all three ratios must be equal. Exam tip: always compare the constant-term ratio along with the coefficient ratios.
Frequently asked questions
What is the correct answer to this question?
Parallel but distinct lines; inconsistent
Why is this the correct answer?
The coefficients of the first equation are 9 times those of the second: \(18/2=27/3=9\). However, the ratio of the constants is \(63/8\), which is not 9. Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are parallel but distinct and the pair is inconsistent; it has no solution. For coincident lines, all three ratios must be equal. Exam tip: always compare the constant-term ratio along with the coefficient ratios.
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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