What is the point of intersection of the lines \(x+y=12\) and \(x-y=4\)?
Answer and explanation
Correct answer: (8, 4)
Adding the two equations gives \(2x=16\), so \(x=8\). Substituting this into \(x+y=12\) gives \(y=4\). Therefore, the point of intersection is \((8,4)\). In option B, \(x-y=4-8=-4\), so it does not satisfy the second equation. Exam tip: Verify a common point by substituting its coordinates into both equations.
Frequently asked questions
What is the correct answer to this question?
(8, 4)
Why is this the correct answer?
Adding the two equations gives \(2x=16\), so \(x=8\). Substituting this into \(x+y=12\) gives \(y=4\). Therefore, the point of intersection is \((8,4)\). In option B, \(x-y=4-8=-4\), so it does not satisfy the second equation. Exam tip: Verify a common point by substituting its coordinates 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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