What type of pair is (11x+4y=18) and (5x+2y=9)?
Answer and explanation
Correct answer: Consistent and independent
For the given equations, \\(a_1/a_2=11/5\\) and \\(b_1/b_2=4/2=2\\). Since \\(11/5 \ne 2\\), the two lines intersect at one point and the pair has a unique solution. Therefore, it is a consistent and independent pair. For a consistent dependent pair, all three ratios are equal. Exam tip: Compare \\(a_1/a_2\\) and \\(b_1/b_2\\) first; if they are unequal, there is exactly one solution.
Frequently asked questions
What is the correct answer to this question?
Consistent and independent
Why is this the correct answer?
For the given equations, \\(a_1/a_2=11/5\\) and \\(b_1/b_2=4/2=2\\). Since \\(11/5 \ne 2\\), the two lines intersect at one point and the pair has a unique solution. Therefore, it is a consistent and independent pair. For a consistent dependent pair, all three ratios are equal. Exam tip: Compare \\(a_1/a_2\\) and \\(b_1/b_2\\) first; if they are unequal, there is exactly one solution.
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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