What is the correct solution status for (6x-7y+13=0) and (18x-21y+40=0)?
Answer and explanation
Correct answer: No solution
Here, \(a_1/a_2=6/18=1/3\) and \(b_1/b_2=(-7)/(-21)=1/3\), whereas \(c_1/c_2=13/40\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), which represents an inconsistent pair of equations. The two lines are distinct and parallel, so they have no solution. Exam tip: Compare the ratios of the coefficients of \(x\), \(y\), and the constants in this order to identify the solution status quickly.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Here, \(a_1/a_2=6/18=1/3\) and \(b_1/b_2=(-7)/(-21)=1/3\), whereas \(c_1/c_2=13/40\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), which represents an inconsistent pair of equations. The two lines are distinct and parallel, so they have no solution. Exam tip: Compare the ratios of the coefficients of \(x\), \(y\), and the constants in this order to identify the solution status quickly.
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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