What is the correct solution status for the equations (12x-7y+29=0) and (36x-21y+91=0)?
Answer and explanation
Correct answer: No solution
Here, \(a_1/a_2=12/36=1/3\) and \(b_1/b_2=(-7)/(-21)=1/3\), but \(c_1/c_2=29/91\), which is not equal to \(1/3\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are parallel and distinct. Therefore, the pair has no solution. Exam tip: First compare the ratios of the coefficients of x and y, and then compare them with the ratio of the constant terms.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Here, \(a_1/a_2=12/36=1/3\) and \(b_1/b_2=(-7)/(-21)=1/3\), but \(c_1/c_2=29/91\), which is not equal to \(1/3\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are parallel and distinct. Therefore, the pair has no solution. Exam tip: First compare the ratios of the coefficients of x and y, and then compare them with the ratio of the constant terms.
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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