For the two variables \(x\) and \(y\), the equations \(5x+5y=140\) and \(6x-6y=24\) are given. In the graphical method, what is the point of intersection of these two lines, i.e. the solution?
Answer and explanation
Correct answer: \((16,12)\)
Dividing the first equation by 5 and the second by 6 gives \(x+y=28\) and \(x-y=4\). Adding these equations yields \(2x=32\), so \(x=16\), and consequently \(y=12\). Therefore, the intersection point of the two lines is \((16,12)\). In option B, the coordinates are reversed; it satisfies \(x+y=28\) but gives \(x-y=-4\), so it is incorrect. Exam tip: In the graphical method, the common point of the two lines represents the solution of the pair of equations.
Frequently asked questions
What is the correct answer to this question?
\((16,12)\)
Why is this the correct answer?
Dividing the first equation by 5 and the second by 6 gives \(x+y=28\) and \(x-y=4\). Adding these equations yields \(2x=32\), so \(x=16\), and consequently \(y=12\). Therefore, the intersection point of the two lines is \((16,12)\). In option B, the coordinates are reversed; it satisfies \(x+y=28\) but gives \(x-y=-4\), so it is incorrect. Exam tip: In the graphical method, the common point of the two lines represents the solution of the pair of 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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