What will (a) be for the equations (9x+ay=63) and (27x+24y=189) to have infinitely many solutions?
Answer and explanation
Correct answer: 8
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, \(\frac{9}{27}=\frac{63}{189}=\frac{1}{3}\), so \(\frac{a}{24}=\frac{1}{3}\), giving \(a=8\). Therefore, option C is correct. Exam tip: For infinitely many solutions, verify equality of all three ratios, not just two of them.
Frequently asked questions
What is the correct answer to this question?
8
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, \(\frac{9}{27}=\frac{63}{189}=\frac{1}{3}\), so \(\frac{a}{24}=\frac{1}{3}\), giving \(a=8\). Therefore, option C is correct. Exam tip: For infinitely many solutions, verify equality of all three ratios, not just two of them.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
