Which situation is represented by (7x+y=10) and (14x+2y=25)?
Answer and explanation
Correct answer: Distinct parallel lines
For the two equations, \(\frac{a_1}{a_2}=\frac{7}{14}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{1}{2}\), whereas \(\frac{c_1}{c_2}=\frac{10}{25}=\frac{2}{5}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), which represents distinct parallel lines. Hence, the pair has no solution; option D states the algebraic consequence, but not the geometrical situation asked here. Exam tip: remember the condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\) for distinct parallel lines.
Frequently asked questions
What is the correct answer to this question?
Distinct parallel lines
Why is this the correct answer?
For the two equations, \(\frac{a_1}{a_2}=\frac{7}{14}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{1}{2}\), whereas \(\frac{c_1}{c_2}=\frac{10}{25}=\frac{2}{5}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), which represents distinct parallel lines. Hence, the pair has no solution; option D states the algebraic consequence, but not the geometrical situation asked here. Exam tip: remember the condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\) for distinct parallel lines.
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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