If the lines \(kx+4y=22\) and \(x+y=6\) intersect at the point \((2,4)\), what is the value of \(k\)?
Answer and explanation
Correct answer: 3
The intersection point \((2,4)\) must satisfy both line equations. Substituting \(x=2\) and \(y=4\) into the first equation gives \(2k+4(4)=22\), or \(2k+16=22\). Hence, \(2k=6\) and \(k=3\), so option B is correct. As a check, the point also satisfies the second equation because \(2+4=6\). Exam tip: when the intersection point is given, substitute its coordinates into the equation containing the unknown parameter.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The intersection point \((2,4)\) must satisfy both line equations. Substituting \(x=2\) and \(y=4\) into the first equation gives \(2k+4(4)=22\), or \(2k+16=22\). Hence, \(2k=6\) and \(k=3\), so option B is correct. As a check, the point also satisfies the second equation because \(2+4=6\). Exam tip: when the intersection point is given, substitute its coordinates into the equation containing the unknown parameter.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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