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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.

**☛ Related Questions:**

- Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction? (ii) Five years ago, Nuri was thrice as old as Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. (iv) Meena went to a bank to withdraw ₹. 2000. She asked the cashier to give her ₹. 50 and ₹. 100 notes Meena got ₹. 25 notes in all. Find how many notes of ₹. 50 and ₹. 100 she received. (v) A lending library has a fixed charge for the first three days and an additional charge for each day Saritha paid ₹. 27 for a book kept for seven days, while Susy paid ₹. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
- Which of the following pairs of linear equations has a unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using the cross multiplication method. (i) x - 3y - 3 = 0; 3x - 9 y - 2 = 0 (ii) 2x + y = 5; 3x + 2 y = 8 (iii) 3x - 5 y =-20; 6x - 10 y = 40 (iv) x - 3y - 7 = 0; 3x - 3y - 15 = 0
- (i) For which values of a and b will the following pair of linear equations have an infinite number of solutions? 2x + 3y = 7 (a - b) x + (a + b) y = 3a + b - 2 (ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1 (2k -1) x + (k -1) y = 2k +1

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