# Solve the following pair of linear equations by the substitution and cross-multiplication methods:

8x + 5y = 9

3x + 2y = 4

**Solution:**

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

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

From equation (2), we obtain

3x + 2 y = 4

3x = 4 - 2 y

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

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

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

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

32 - y = 27

y = 32 - 27

y = 5

x = (4 - 2 × 5)/3

x = -6/-3

x = 2

Hence, x = - 2, y = 5

Again, by cross-multiplication method

8x + 5y = 9

3x + 2y = 4

8x + 5 y - 9 = 0

3x + 2 y - 4 = 0

a1 = 8, b1 = 5, c1 = - 9

a2 = 3, b2 = 2, c2 = - 4

[x/(b_{1}c_{2}- b_{2}c_{1}) = y/(c_{1}a_{2}- c_{2}a_{1}) = 1/(a_{1}b_{2} - a_{2}b_{1})]

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

x/-2 = y/5 = 1

x = - 2 and y = 5

**Video Solution:**

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

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

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

On solving the pair of lines that are 8x + 5 y = 9 and 3x + 2 y = 4 we get x = -2, and y = 5.