Which is the graphical solution of (2x + y = 11) and (x + y = 8)?
Answer and explanation
Correct answer: (3, 5)
The graphical solution of two linear equations is their common point, or the point where the two corresponding lines intersect. We can verify each candidate by substitution. For (3, 5), the first equation gives 2(3) + 5 = 6 + 5 = 11, and the second gives 3 + 5 = 8. Therefore (3, 5) lies on both lines and is their intersection point. Option B is correct. For (5, 3), the first equation gives 13; for (4, 4), it gives 12; and for (2, 6), it gives 10, so those points fail the first equation even though some may satisfy the second. Since a graphical solution must satisfy both equations simultaneously, only option B is valid.
Frequently asked questions
What is the correct answer to this question?
(3, 5)
Why is this the correct answer?
The graphical solution of two linear equations is their common point, or the point where the two corresponding lines intersect. We can verify each candidate by substitution. For (3, 5), the first equation gives 2(3) + 5 = 6 + 5 = 11, and the second gives 3 + 5 = 8. Therefore (3, 5) lies on both lines and is their intersection point. Option B is correct. For (5, 3), the first equation gives 13; for (4, 4), it gives 12; and for (2, 6), it gives 10, so those points fail the first equation even though some may satisfy the second. Since a graphical solution must satisfy both equations simultaneously, only option B is valid.
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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