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two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically.
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Most Upvoted Answer
two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.rep...
The lines are parallel since slopes are equal (-1/2).
The slope of a line (ax+by+c=0) is (-a/b).
Hence the slopes of both lines are -0.5
Hence they are parallel as the constant terms are not equal.
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two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.rep...
Understanding the Linear Equations
The two given equations represent linear equations in two variables:
- Equation 1: x + 2y - 4 = 0
- Equation 2: 2x + 4y - 12 = 0
Forming the Graph
To represent these equations geometrically, we can rearrange them into the slope-intercept form (y = mx + b).
- For Equation 1:
Rearranging gives:
2y = -x + 4
y = -1/2 x + 2
- For Equation 2:
Rearranging gives:
4y = -2x + 12
y = -1/2 x + 3
Identifying Characteristics
- Slope: Both equations have the same slope of -1/2, indicating that the lines are parallel.
- Y-Intercept: The first line intercepts the y-axis at (0, 2), while the second line intercepts at (0, 3).
Geometric Representation
- Parallel Lines: Since both lines have the same slope, they will never intersect, confirming they represent parallel rails in a geometrical sense.
- Visual Appeal: Plotting these equations on a Cartesian plane will show two distinct lines running parallel to each other without any points of intersection.
Conclusion
By graphing these equations, we can visually understand that they represent two parallel rails, emphasizing the concept of parallel lines in the context of linear equations. This analysis aligns with the principles discussed in the NCERT Class 10 curriculum on pairs of linear equations in two variables.
The two given equations represent linear equations in two variables:
- Equation 1: x + 2y - 4 = 0
- Equation 2: 2x + 4y - 12 = 0
Forming the Graph
To represent these equations geometrically, we can rearrange them into the slope-intercept form (y = mx + b).
- For Equation 1:
Rearranging gives:
2y = -x + 4
y = -1/2 x + 2
- For Equation 2:
Rearranging gives:
4y = -2x + 12
y = -1/2 x + 3
Identifying Characteristics
- Slope: Both equations have the same slope of -1/2, indicating that the lines are parallel.
- Y-Intercept: The first line intercepts the y-axis at (0, 2), while the second line intercepts at (0, 3).
Geometric Representation
- Parallel Lines: Since both lines have the same slope, they will never intersect, confirming they represent parallel rails in a geometrical sense.
- Visual Appeal: Plotting these equations on a Cartesian plane will show two distinct lines running parallel to each other without any points of intersection.
Conclusion
By graphing these equations, we can visually understand that they represent two parallel rails, emphasizing the concept of parallel lines in the context of linear equations. This analysis aligns with the principles discussed in the NCERT Class 10 curriculum on pairs of linear equations in two variables.
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two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically. Related: Ex 3.1 NCERT Solutions - Pair of Linear Equations in Two Variables? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically. Related: Ex 3.1 NCERT Solutions - Pair of Linear Equations in Two Variables? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically. Related: Ex 3.1 NCERT Solutions - Pair of Linear Equations in Two Variables?.
two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically. Related: Ex 3.1 NCERT Solutions - Pair of Linear Equations in Two Variables? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically. Related: Ex 3.1 NCERT Solutions - Pair of Linear Equations in Two Variables? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for two rails are represented by the equation x+2y-4=0 and 2x+4y-12=0.represent this situation geometrically. Related: Ex 3.1 NCERT Solutions - Pair of Linear Equations in Two Variables?.
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