If the lines \(2x+y=16\) and \(x+y=10\) are drawn on a graph, what will be their point of intersection?
Answer and explanation
Correct answer: \((6,4)\)
The point of intersection must satisfy both linear equations simultaneously. Substituting \((6,4)\) gives \(2(6)+4=16\) and \(6+4=10\), so it is the graphical solution. For example, \((5,5)\) satisfies the second equation but not the first. Exam tip: verify a proposed intersection point by substituting its coordinates into both equations.
Frequently asked questions
What is the correct answer to this question?
\((6,4)\)
Why is this the correct answer?
The point of intersection must satisfy both linear equations simultaneously. Substituting \((6,4)\) gives \(2(6)+4=16\) and \(6+4=10\), so it is the graphical solution. For example, \((5,5)\) satisfies the second equation but not the first. Exam tip: verify a proposed intersection 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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