For prices of two items, the equations (9x+4y=360) and (27x+12y=1090) are formed. What type of system is this?
Answer and explanation
Correct answer: Inconsistent
Here, \(\frac{a_1}{a_2}=\frac{9}{27}=\frac{1}{3}\) and \(\frac{b_1}{b_2}=\frac{4}{12}=\frac{1}{3}\), but \(\frac{c_1}{c_2}=\frac{360}{1090}\neq\frac{1}{3}\). Thus, the two lines are distinct and parallel, so they have no solution and the system is inconsistent. Option B would be correct only if all three ratios were equal, giving infinitely many solutions. Exam tip: When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), the system is inconsistent.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
Here, \(\frac{a_1}{a_2}=\frac{9}{27}=\frac{1}{3}\) and \(\frac{b_1}{b_2}=\frac{4}{12}=\frac{1}{3}\), but \(\frac{c_1}{c_2}=\frac{360}{1090}\neq\frac{1}{3}\). Thus, the two lines are distinct and parallel, so they have no solution and the system is inconsistent. Option B would be correct only if all three ratios were equal, giving infinitely many solutions. Exam tip: When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), the system is inconsistent.
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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