Let x and y be two numbers. Three times their sum is 60 and twice their difference is 12; that is, 3x + 3y = 60 and 2x − 2y = 12. What is the solution (x, y) obtained by the graphical method?
Answer and explanation
Correct answer: (13, 7)
Dividing the equations by 3 and 2 respectively gives x + y = 20 and x − y = 6. Adding these equations gives 2x = 26, so x = 13 and y = 7. Thus, the intersection point of the two lines is (13, 7). Option B has the correct sum but gives a difference of −6, not 6. Exam tip: In the graphical method, the point where the two lines intersect represents the solution of the pair of equations.
Frequently asked questions
What is the correct answer to this question?
(13, 7)
Why is this the correct answer?
Dividing the equations by 3 and 2 respectively gives x + y = 20 and x − y = 6. Adding these equations gives 2x = 26, so x = 13 and y = 7. Thus, the intersection point of the two lines is (13, 7). Option B has the correct sum but gives a difference of −6, not 6. Exam tip: In the graphical method, the point where the two lines intersect 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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