If (kx+3y=25) and (x-y=2) have solution (x=5,\ y=3), what is the value of (k)?
Answer and explanation
Correct answer: \(k=\frac{16}{5}\)
The given solution \(x=5, y=3\) must satisfy \(kx+3y=25\). Thus, \(5k+3(3)=25\), so \(5k+9=25\). Hence \(5k=16\) and \(k=\frac{16}{5}\). For instance, using \(k=\frac{14}{5}\) makes the left-hand side \(23\), not \(25\). Exam tip: when a solution is given, substitute its values directly into the original equation.
Frequently asked questions
What is the correct answer to this question?
\(k=\frac{16}{5}\)
Why is this the correct answer?
The given solution \(x=5, y=3\) must satisfy \(kx+3y=25\). Thus, \(5k+3(3)=25\), so \(5k+9=25\). Hence \(5k=16\) and \(k=\frac{16}{5}\). For instance, using \(k=\frac{14}{5}\) makes the left-hand side \(23\), not \(25\). Exam tip: when a solution is given, substitute its values directly into the original equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
