For two variables x and y, the linear equations 3x + 3y = 99 and 4x − 4y = 28 are given. What is the solution of these equations by the graphical method?
Answer and explanation
Correct answer: (20, 13)
Dividing the first equation by 3 and the second by 4 gives x + y = 33 and x − y = 7. Adding these equations gives 2x = 40, so x = 20 and y = 13. Therefore, the intersection point of the two lines, and hence the graphical solution, is (20, 13). Option B reverses the coordinates; for (13, 20), x − y = −7, so it is incorrect. Exam tip: the point where the two graphs intersect represents the solution of the pair of linear equations.
Frequently asked questions
What is the correct answer to this question?
(20, 13)
Why is this the correct answer?
Dividing the first equation by 3 and the second by 4 gives x + y = 33 and x − y = 7. Adding these equations gives 2x = 40, so x = 20 and y = 13. Therefore, the intersection point of the two lines, and hence the graphical solution, is (20, 13). Option B reverses the coordinates; for (13, 20), x − y = −7, so it is incorrect. Exam tip: the point where the two graphs intersect represents the solution of the pair of linear 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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