text: Class 10
  MATHS
  Pair Of Linear Equations In Two Variables
  
  Determine graphically, the vertices of the triangle formed by the lines <br> y=x, 3y=x and x+y=8
  
  Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
  
  Updated On: 26-8-2020
  
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  Text Solution
  
  Solution :
  Given linear equations are <br> y=x " " ...(i) <br> 3y=x " " ...(ii) <br> and X+y=8 " " ...(iii) <br> For equation y=x, <br> If x=1, then y=1 <br> If x=0, then y=0 <br> If x=2, then y=2 <br> Table for line y=x, <br> {:(" "x,0,1,2),(" "y,0,1,2),("Points","O","A","B"):} <br> For equation x=3y , <br> If x=0, then y=0, if x=3, then y=1 and if x=6, then y=2 <br> Table for line x=3y, <br> {:(" "x,0,3,6),(" "y,0,1,2),("Points","O","C","D"):} <br> For equation " " x+y=8 rArr y=8-x <br> If x=0, then y=8, if x=8, then y=0 and if x=4, then y=4 <br> Table for line x+y=8,. <br> {:(" "x,0,4,8),(" "y,8,4,0),("Points","P","Q","R"):} <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_X_C03_S01_043_S01.png" width="80%"> <br> Plotting the points A(1, 1) and B(2, 2), we get the straight line AB. Plotting C(3, 1) and D(6,2), we get the straight line CD. Plotting the points P(0, 8), Q(4, 4) and R(8, 0), we get the straight line PQR. We see that lines AB and CD intersecting the line PR on Q and D,respectively. <br> So, DeltaOQD is formed by these lines. Hence, the vertices of the DeltaOQD formed by the given lines are O(0, 0), Q(4, 4) and D(6, 2).
  
  Image Solution
  
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explanation: The document contains a math question and its detailed solution. The question asks to determine graphically the vertices of the triangle formed by the lines \( y = x \), \( 3y = x \), and \( x + y = 8 \). The solution provides step-by-step reasoning and includes tables and a graph to illustrate the points of intersection and the vertices of the triangle.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Class 10
  MATHS
  Pair Of Linear Equations In Two Variables
  
  Determine graphically, the vertices of the triangle formed by the lines <br> y=x, 3y=x and x+y=8
  
  Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
  
  Updated On: 26-8-2020
  
  Apne doubts clear karein ab Whatsapp par bhi. Try it now.
  
  Watch 1000+ concepts & tricky questions explained!
  
  83.2 K+
  
  4.1 K+
  
  Text Solution
  
  Solution :
  Given linear equations are <br> y=x " " ...(i) <br> 3y=x " " ...(ii) <br> and X+y=8 " " ...(iii) <br> For equation y=x, <br> If x=1, then y=1 <br> If x=0, then y=0 <br> If x=2, then y=2 <br> Table for line y=x, <br> {:(" "x,0,1,2),(" "y,0,1,2),("Points","O","A","B"):} <br> For equation x=3y , <br> If x=0, then y=0, if x=3, then y=1 and if x=6, then y=2 <br> Table for line x=3y, <br> {:(" "x,0,3,6),(" "y,0,1,2),("Points","O","C","D"):} <br> For equation " " x+y=8 rArr y=8-x <br> If x=0, then y=8, if x=8, then y=0 and if x=4, then y=4 <br> Table for line x+y=8,. <br> {:(" "x,0,4,8),(" "y,8,4,0),("Points","P","Q","R"):} <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_X_C03_S01_043_S01.png" width="80%"> <br> Plotting the points A(1, 1) and B(2, 2), we get the straight line AB. Plotting C(3, 1) and D(6,2), we get the straight line CD. Plotting the points P(0, 8), Q(4, 4) and R(8, 0), we get the straight line PQR. We see that lines AB and CD intersecting the line PR on Q and D,respectively. <br> So, DeltaOQD is formed by these lines. Hence, the vertices of the DeltaOQD formed by the given lines are O(0, 0), Q(4, 4) and D(6, 2).
  
  Image Solution
  
  1384244
  
  119.5 K+
  
  231.3 K+
  
  4:04
  26861796
  
  3.1 K+
  
  61.5 K+
  
  3:34
  1409821
  
  13.0 K+
  
  261.0 K+
  
  9:30
  1384256
  
  56.7 K+
  
  68.7 K+
  
  3:50
  1409812
  
  12.5 K+
  
  250.0 K+
  
  9:23
  1131478
  
  10.6 K+
  
  213.4 K+
  
  2:59
  31343778
  
  1.7 K+
  
  34.4 K+
  
  1:29
  61732755
  
  3.9 K+
  
  79.7 K+
  
  39300
  
  10.7 K+
  
  215.0 K+
  
  7:41
  1189117
  
  2.1 K+
  
  43.1 K+
  
  2:19
  8491106
  
  15.8 K+
  
  30.7 K+
  
  7:58
  1118041
  
  134.1 K+
  
  177.2 K+
  
  5:43
  39301
  
  9.3 K+
  
  186.4 K+
  
  4:01
  1448793
  
  102.7 K+
  
  331.9 K+
  
  3:30
  57451
  
  9.6 K+
  
  192.9 K+
  
  5:10
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its detailed solution. The question asks to determine graphically the vertices of the triangle formed by the lines \( y = x \), \( 3y = x \), and \( x + y = 8 \). The solution provides step-by-step reasoning and includes tables and a graph to illustrate the points of intersection and the vertices of the triangle.
  
  Label: question-and-answer