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

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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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The text passage contains a mathematical question about determining the vertices of a triangle formed by the intersection of three given linear equations. The solution to the problem is provided in the text, including the vertices of the triangle.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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
user
The text passage contains a mathematical question about determining the vertices of a triangle formed by the intersection of three given linear equations. The solution to the problem is provided in the text, including the vertices of the triangle.

TYPE: SINGLE_QUESTION_WITH_ANSWER