A day full of math games & activities. Find one near you.

43x + 67y = - 24, 67x + 43y = 24, solve the equation

Solution:

From the above question, we have the linear equations as,

43x + 67y = -24----------------------(1)

and 67x + 43y = 24-----------------(2)

Multiplying (1) by 43 and (2) by 67 and Subtracting both of them, we get,

{(67)² - (43)²}x = 24(67 + 43)

Since,(a² - b²) = (a - b)(a + b),we get,

(67 + 43)(67 - 43)x = 24 × 110

110 × 24x = 24 × 110

x = 1.

Substituting the x value in eq. (1), we get,

43 × 1 + 67y = -24

67y = -24 - 43

67y = -67

y = -1.

x = 1.

y = -1.

Therefore, the required values of x and y are 1 and -1, respectively.

✦ Try This: Solve the following equation: 43x + 67y = - 22, 67x + 43y = 22

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 9 (v)

Summary:

Solving the following equation 43x + 67y = - 24, 67x + 43y = 24, we get the required values of x and y as 1 and -1, respectively.

☛ Related Questions: