What is the correct solution status for the equations (6x-4y+11=0) and (15x-10y+28=0)?
Answer and explanation
Correct answer: No solution
Here, \(a_1=6, b_1=-4, c_1=11\) and \(a_2=15, b_2=-10, c_2=28\). We have \(\frac{a_1}{a_2}=\frac{6}{15}=\frac{2}{5}\) and \(\frac{b_1}{b_2}=\frac{-4}{-10}=\frac{2}{5}\), but \(\frac{c_1}{c_2}=\frac{11}{28}\), which is not equal to \(\frac{2}{5}\). Thus, the two lines are distinct and parallel, so they do not intersect. Therefore, the pair has no solution. Exam tip: If \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the lines are parallel and the pair has no solution.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Here, \(a_1=6, b_1=-4, c_1=11\) and \(a_2=15, b_2=-10, c_2=28\). We have \(\frac{a_1}{a_2}=\frac{6}{15}=\frac{2}{5}\) and \(\frac{b_1}{b_2}=\frac{-4}{-10}=\frac{2}{5}\), but \(\frac{c_1}{c_2}=\frac{11}{28}\), which is not equal to \(\frac{2}{5}\). Thus, the two lines are distinct and parallel, so they do not intersect. Therefore, the pair has no solution. Exam tip: If \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the lines are parallel and the pair has no 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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