For prices of two tickets, the equations (8x+3y=280) and (16x+6y=575) are formed. What type of system is this?
Answer and explanation
Correct answer: Having no solution
The ratios of the coefficients are \(\frac{8}{16}=\frac{3}{6}=\frac{1}{2}\), but the ratio of the constant terms is \(\frac{280}{575}=\frac{56}{115}\neq\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), so the two lines are parallel and have no common solution; the system is inconsistent. Option B would be correct only if all three ratios were equal, giving infinitely many solutions. Exam tip: Compare the three coefficient and constant ratios directly to identify the type of system quickly.
Frequently asked questions
What is the correct answer to this question?
Having no solution
Why is this the correct answer?
The ratios of the coefficients are \(\frac{8}{16}=\frac{3}{6}=\frac{1}{2}\), but the ratio of the constant terms is \(\frac{280}{575}=\frac{56}{115}\neq\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), so the two lines are parallel and have no common solution; the system is inconsistent. Option B would be correct only if all three ratios were equal, giving infinitely many solutions. Exam tip: Compare the three coefficient and constant ratios directly to identify the type of system 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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