What is the point of intersection of the lines \(x+y=16\) and \(x-y=6\)?
Answer and explanation
Correct answer: (11, 5)
Adding the two equations gives \(2x=22\), so \(x=11\). Substituting this into \(x+y=16\) gives \(y=5\). Therefore, the intersection point is \((11,5)\). Option B has the coordinates reversed; although \(5+11=16\), \(5-11\neq6\). Exam tip: Always substitute a proposed point into both equations.
Frequently asked questions
What is the correct answer to this question?
(11, 5)
Why is this the correct answer?
Adding the two equations gives \(2x=22\), so \(x=11\). Substituting this into \(x+y=16\) gives \(y=5\). Therefore, the intersection point is \((11,5)\). Option B has the coordinates reversed; although \(5+11=16\), \(5-11\neq6\). Exam tip: Always substitute a proposed point into both equations.
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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