If the pair of linear equations \(x+y=8\) and \(kx+2y=14\) passes through the point \((2,6)\), what is the value of \(k\)?
Answer and explanation
Correct answer: 1
The point \((2,6)\) satisfies the first equation because \(2+6=8\). Substituting \(x=2\) and \(y=6\) into the second equation gives \(2k+2(6)=14\), or \(2k+12=14\). Thus, \(2k=2\) and \(k=1\). Therefore, option A is correct. Exam tip: To test whether a point lies on a line, substitute its coordinates directly into the equation.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The point \((2,6)\) satisfies the first equation because \(2+6=8\). Substituting \(x=2\) and \(y=6\) into the second equation gives \(2k+2(6)=14\), or \(2k+12=14\). Thus, \(2k=2\) and \(k=1\). Therefore, option A is correct. Exam tip: To test whether a point lies on a line, substitute its coordinates directly into the 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: Graphical method of finding solutions..
