For infinitely many solutions of (jx+5y=10) and (14x+7y=14), what is (j)?
Answer and explanation
Correct answer: \(j=10\)
For infinitely many solutions, the two linear equations must represent the same line; hence \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{5}{7}=\frac{10}{14}\), so \(\frac{j}{14}=\frac{5}{7}\). Therefore, \(j=10\). For example, if \(j=8\), then \(\frac{j}{14}\neq\frac{5}{7}\), so the equations cannot have infinitely many solutions. Exam tip: for infinitely many solutions, verify that all three ratios are equal.
Frequently asked questions
What is the correct answer to this question?
\(j=10\)
Why is this the correct answer?
For infinitely many solutions, the two linear equations must represent the same line; hence \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{5}{7}=\frac{10}{14}\), so \(\frac{j}{14}=\frac{5}{7}\). Therefore, \(j=10\). For example, if \(j=8\), then \(\frac{j}{14}\neq\frac{5}{7}\), so the equations cannot have infinitely many solutions. Exam tip: for infinitely many solutions, verify that all three ratios are equal.
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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