For prices of two items, the equations (6x+5y=240) and (12x+10y=490) are formed. What type of system is this?
Answer and explanation
Correct answer: Inconsistent
Here, \(a_1/a_2=6/12=1/2\), while \(b_1/b_2=5/10=1/2\) and \(c_1/c_2=240/490=24/49\). Thus, \(a_1/a_2=b_1/b_2\neq c_1/c_2\), so the two lines are distinct and parallel and have no common solution. Therefore, the system is inconsistent. It is not consistent and dependent, because that case requires all three ratios to be equal and gives infinitely many solutions. Exam tip: Compare all three corresponding ratios in such questions.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
Here, \(a_1/a_2=6/12=1/2\), while \(b_1/b_2=5/10=1/2\) and \(c_1/c_2=240/490=24/49\). Thus, \(a_1/a_2=b_1/b_2\neq c_1/c_2\), so the two lines are distinct and parallel and have no common solution. Therefore, the system is inconsistent. It is not consistent and dependent, because that case requires all three ratios to be equal and gives infinitely many solutions. Exam tip: Compare all three corresponding ratios in such questions.
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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