What is the graphical solution of the two lines represented by 3x − y = 7 and x + y = 5?
Answer and explanation
Correct answer: (3, 2)
In the graphical method, the intersection point of the two lines is the solution of the pair of equations. Adding the equations gives 4x = 12, so x = 3. Substituting this in x + y = 5 gives y = 2. Therefore, the intersection point is (3, 2). The nearby option (2, 3) is incorrect because 3(2) − 3 = 3, not 7. Exam tip: Verify a coordinate pair in both equations before selecting the answer.
Frequently asked questions
What is the correct answer to this question?
(3, 2)
Why is this the correct answer?
In the graphical method, the intersection point of the two lines is the solution of the pair of equations. Adding the equations gives 4x = 12, so x = 3. Substituting this in x + y = 5 gives y = 2. Therefore, the intersection point is (3, 2). The nearby option (2, 3) is incorrect because 3(2) − 3 = 3, not 7. Exam tip: Verify a coordinate pair in both equations before selecting the answer.
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..
