What will be the graph of (2x+y=4) and (6x+3y=10)?
Answer and explanation
Correct answer: Distinct parallel lines
For the two equations, \(\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}\) and \(\frac{b_1}{b_2}=\frac{1}{3}\), but \(\frac{c_1}{c_2}=\frac{4}{10}=\frac{2}{5}\). 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 represented by distinct parallel lines. Therefore, option C is correct. Exam tip: if all three ratios are equal, the lines are coincident; if only the first two are equal, they are distinct parallel lines.
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What is the correct answer to this question?
Distinct parallel lines
Why is this the correct answer?
For the two equations, \(\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}\) and \(\frac{b_1}{b_2}=\frac{1}{3}\), but \(\frac{c_1}{c_2}=\frac{4}{10}=\frac{2}{5}\). 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 represented by distinct parallel lines. Therefore, option C is correct. Exam tip: if all three ratios are equal, the lines are coincident; if only the first two are equal, they are 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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