What is the value of (a) for the equations (6x+ay=42) and (18x+33y=126) to have infinitely many solutions?
Answer and explanation
Correct answer: 11
For two linear equations to have infinitely many solutions, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{6}{18}=\frac{42}{126}=\frac{1}{3}\). Therefore, \(\frac{a}{33}=\frac{1}{3}\), giving \(a=11\). Hence, option C is correct. Exam tip: For infinitely many solutions, the ratios of the corresponding coefficients and constant terms must all be equal; checking only one ratio is not sufficient.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{6}{18}=\frac{42}{126}=\frac{1}{3}\). Therefore, \(\frac{a}{33}=\frac{1}{3}\), giving \(a=11\). Hence, option C is correct. Exam tip: For infinitely many solutions, the ratios of the corresponding coefficients and constant terms must all be equal; checking only one ratio 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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