Class 10 Exam > Class 10 Questions > Graphically, the pair of equations6x – 3y + ...
Start Learning for Free
Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
Represents two lines which are:
- a)Intersecting at exactly one point
- b)Intersecting at exactly two points
- c)Coincident
- d)Parallel
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Repre...
Here,
View all questions of this test
a1 / a2 = 6 / 2 = 3 / 1
b1 / b2 = -3 / -1 = 3 / 1
c1 / c2 = 10 / 9
This implies
a1 / a2 = b1 / b2 ≠ c1 / c2
Most Upvoted Answer
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Repre...
Given equations:
Equation 1: 6x - 3y + 10 = 0
Equation 2: 2x - y + 9 = 0
Graphical representation:
To determine the graphical representation of the given equations, we need to convert them into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Converting Equation 1:
6x - 3y + 10 = 0
-3y = -6x - 10
y = 2x + (10/3)
Converting Equation 2:
2x - y + 9 = 0
-y = -2x - 9
y = 2x + 9
Explanation:
The slope-intercept form of Equation 1 is y = 2x + (10/3), which indicates that the slope of the line is 2. Similarly, the slope-intercept form of Equation 2 is y = 2x + 9, which also indicates a slope of 2.
Since the slopes of both lines are equal, but the y-intercepts are different, the lines are parallel. When two lines are parallel, they never intersect. Hence, the correct answer is option D, "Parallel".
Graphical representation:
To visually represent the lines on a graph, we can plot a few points and connect them to form the lines.
For Equation 1:
Let's assume x = 0, then y = (10/3) [point (0, 10/3)]
Let's assume x = 3, then y = 8 [point (3, 8)]
For Equation 2:
Let's assume x = 0, then y = 9 [point (0, 9)]
Let's assume x = 3, then y = 15 [point (3, 15)]
Plotting these points on a graph, we can see that the lines never intersect and run parallel to each other.
Equation 1: 6x - 3y + 10 = 0
Equation 2: 2x - y + 9 = 0
Graphical representation:
To determine the graphical representation of the given equations, we need to convert them into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Converting Equation 1:
6x - 3y + 10 = 0
-3y = -6x - 10
y = 2x + (10/3)
Converting Equation 2:
2x - y + 9 = 0
-y = -2x - 9
y = 2x + 9
Explanation:
The slope-intercept form of Equation 1 is y = 2x + (10/3), which indicates that the slope of the line is 2. Similarly, the slope-intercept form of Equation 2 is y = 2x + 9, which also indicates a slope of 2.
Since the slopes of both lines are equal, but the y-intercepts are different, the lines are parallel. When two lines are parallel, they never intersect. Hence, the correct answer is option D, "Parallel".
Graphical representation:
To visually represent the lines on a graph, we can plot a few points and connect them to form the lines.
For Equation 1:
Let's assume x = 0, then y = (10/3) [point (0, 10/3)]
Let's assume x = 3, then y = 8 [point (3, 8)]
For Equation 2:
Let's assume x = 0, then y = 9 [point (0, 9)]
Let's assume x = 3, then y = 15 [point (3, 15)]
Plotting these points on a graph, we can see that the lines never intersect and run parallel to each other.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer?
Question Description
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer?.
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Graphically, the pair of equations6x – 3y + 10 = 02x – y + 9 = 0Represents two lines which are:a)Intersecting at exactly one pointb)Intersecting at exactly two pointsc)Coincidentd)ParallelCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup