What is the graphical solution, that is, the point of intersection of the lines \(x+3y=15\) and \(x+y=7\)?
Answer and explanation
Correct answer: (3,4)
The coordinates of the intersection point must satisfy both equations. Subtracting the second equation from the first gives \((x+3y)-(x+y)=15-7\), so \(2y=8\) and \(y=4\). Using \(x+y=7\), we get \(x=3\). Therefore, the intersection point is \((3,4)\). For example, the close distractor \((4,3)\) satisfies the second equation but not the first. Exam tip: The graphical solution is the common point of both lines.
Frequently asked questions
What is the correct answer to this question?
(3,4)
Why is this the correct answer?
The coordinates of the intersection point must satisfy both equations. Subtracting the second equation from the first gives \((x+3y)-(x+y)=15-7\), so \(2y=8\) and \(y=4\). Using \(x+y=7\), we get \(x=3\). Therefore, the intersection point is \((3,4)\). For example, the close distractor \((4,3)\) satisfies the second equation but not the first. Exam tip: The graphical solution is the common point of both lines.
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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