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Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9
3x + 2y = 4

Solution:

8x + 5y = 9 .....(1)

3x + 2y = 4....(2)

From equation (2), we obtain

3x + 2y = 4

3x = 4 - 2y

x = (4 - 2y)/3 ....(3)

Substituting x = (4 - 2y)/3 in equation (1), we obtain

8[(4 - 2y)/3] + 5y = 9

(32 - 16y + 15y)/3 = 9

32 - y = 27

y = 32 - 27

y = 5

Thus, x = (4 - 2 × 5)/3 [From equation(3)]

x = -6/3

x = - 2

Hence, x = - 2, y = 5

Again, by cross-multiplication method

8x + 5y = 9

3x + 2y = 4

8x + 5  - 9 = 0

3x + 2  - 4 = 0

a₁ = 8, b₁ = 5, c₁ = - 9

a₂ = 3, b₂ = 2, c₂ = - 4

[x/(b₁c₂ - b₂c₁) = y/(c₁a₂ - c₂a₁) = 1/(a₁b₂ - a₂b₁)]

x/[-20 - (-18)] = y/[-27 - (-32)] = 1/(16 - 15)

x/(-2) = y/5 = 1

x = - 2 and y = 5

☛ Check: NCERT Solutions Class 10 Maths Chapter 3

Video Solution:

Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9; 3x + 2 y = 4

NCERT Solutions for Class 10 Maths - Chapter 3 Exercise 3.5 Question 3

Summary:

On solving the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5 y = 9 and 3x + 2 y = 4 we get x = - 2, and y = 5.

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