What is the relation among all three ratios in the equations (9x+16y=74) and (27x+48y=222)?
Answer and explanation
Correct answer: All three ratios are equal
The ratios of the corresponding coefficients and constants are \(\frac{9}{27}=\frac{16}{48}=\frac{74}{222}=\frac{1}{3}\). Hence, all three ratios are equal. When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), the two linear equations represent the same line and have infinitely many solutions. Exam tip: Always compare the ratio of the constant terms as well; checking only the coefficients of x and y is not sufficient.
Frequently asked questions
What is the correct answer to this question?
All three ratios are equal
Why is this the correct answer?
The ratios of the corresponding coefficients and constants are \(\frac{9}{27}=\frac{16}{48}=\frac{74}{222}=\frac{1}{3}\). Hence, all three ratios are equal. When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), the two linear equations represent the same line and have infinitely many solutions. Exam tip: Always compare the ratio of the constant terms as well; checking only the coefficients of x and y is not sufficient.
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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