# HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

## AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Book Answers AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Book Answers

## Andhra Pradesh State Board Class 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Books Solutions

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## AP Board Class 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbooks Solutions with Answer PDF Download

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### 10th Class Maths 4th Lesson Pair of Linear Equations in Two Variables Optional Exercise Textbook Questions and Answers

Question 1.
i) 2𝑥𝑎 + 𝑦𝑏 = 2
𝑥𝑎 – 𝑦𝑏 = 4 Substituting x = 2a in the equation (1) we get
2𝑎(2a) + 𝑦𝑏 = 2
⇒ 4 + 𝑦𝑏 = 2
⇒ 𝑦𝑏 = -2
⇒ y = -2b
∴ The solution (x, y) = (2a, -2b)

ii) 𝑥+12 + 𝑦−13 = 8
𝑥−13 + 𝑦+12 = 9
Given: 𝑥+12 + 𝑦−13 = 8 ⇒ 3x + 2y + 1 = 48
⇒ 3x + 2y = 47 …… (1)
and 𝑥−13 + 𝑦+12 = 9 ⇒ 2x + 3y + 1 = 54
⇒ 2x + 3y = 53 …… (2) ⇒ y = −65−5 = 13
Substituting y = 13 in equation (1) we get
3x + 2(13) = 47
⇒ 3x = 47 – 26
⇒ 3x = 21
⇒ x = 213 = 7
∴ The solution (x, y) = (7, 13)

iii) 𝑥7 + 𝑦3 = 5
𝑥2 – 𝑦9 = 6
Given: 𝑥7 + 𝑦3 = 5 and 𝑥2 – 𝑦9 = 6
⇒ 3𝑥+7𝑦21 = 5 and 9𝑥−2𝑦18 = 6
⇒ 3x + 7y = 105 …….. (1) and
9x – 2y = 108 …….. (2) ⇒ y = 20723 = 9
Substituting y = 9 in equation (1) we get
3x + 7(9) = 105
⇒ 3x = 105 – 63
⇒ 3x = 42
⇒ x = 423 = 14
∴ The solution (x, y) = (14, 9)

iv) √3x + √2y = √3
√5x + √3y= √3
Given that √3x + √2y = √3 …… (1)
√5x + √3y = √3 …… (2)
By following elimination method Now again following elimination method ∴ The solution x = 3−6√3−10√ and y = 3−15√3−10√

v) 𝑎𝑥𝑏 + 𝑏𝑦𝑎 = a + b
ax – by = 2ab
Given: 𝑎𝑥𝑏 + 𝑏𝑦𝑎 = a + b ……. (1)
ax – by = 2ab …….. (2) Substituting y = – a in equation (2)
we get ax – b(-a) = 2ab
ax + ab = 2ab
ax = 2ab – ab = ab
⇒ x = 𝑎𝑏𝑎 = b
∴ (x, y) = (b, -a)

vi) 2x + 3y = 17
2x+2 – 3y+1 = 5
Given: 2x + 3y = 17 and
2x+2 – 3y+1 = 5
Take 2x = a and 3y = b then the given equations reduce to
2x + 3y = 17 ⇒ a + b = 17 …… (1)
2x . 22 – 3y . 3 = 5 ⇒ 4a – 3b = 5 …… (2) Substituting b = 9 in equation (1) we get
a + 9 = 17 ⇒ a = 17 – 9 = 8
But a = 2x – 8 and b = 3y = 9
⇒ 2x = 23 and 3y = 32
⇒ x = 3 and y = 2
∴ The solution (x, y) is (3, 2)

Question 2.
Animals in an experiment are to be kept on a strict diet. Each animal is to receive among other things 20g of protein and 6g of fat. The laboratory technicians purchased two food mixes, A and B. Mix A has 10% protein and 6% fat. Mix B has 20% protein and 2% fat. How many grams of each mix should be used?
Let x gms of mix A and y gms of mix B are to be mixed, then  Substituting y = 60 in equation (1)
we get x + 2 × 60 = 200
⇒ x + 120 = 200
⇒ x = 200 – 120 = 80 gm
∴ Quantity of mix. A = 80 gms.
Quantity of mix. B = 60 gms.

## Andhra Pradesh Board Class 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise exam preparation. The AP Board STD 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Books State Board syllabus with maximum efficiency.

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