What will (q) be for (7x+qy=29) and (14x+10y=58) to have infinitely many solutions?
Answer and explanation
Correct answer: \(5\)
For infinitely many solutions, the two linear equations must represent the same line, so one equation must be a multiple of the other. Here, \(14x+10y=58\) must be twice the first equation. Thus, \(2q=10\), giving \(q=5\). With a close option such as \(q=4\), the coefficients of \(y\) would not be in the same ratio, so infinitely many solutions would not occur. Exam tip: for infinitely many solutions, check \(a_1/a_2=b_1/b_2=c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
\(5\)
Why is this the correct answer?
For infinitely many solutions, the two linear equations must represent the same line, so one equation must be a multiple of the other. Here, \(14x+10y=58\) must be twice the first equation. Thus, \(2q=10\), giving \(q=5\). With a close option such as \(q=4\), the coefficients of \(y\) would not be in the same ratio, so infinitely many solutions would not occur. Exam tip: for infinitely many solutions, check \(a_1/a_2=b_1/b_2=c_1/c_2\).
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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