Question

Solve the following pair of equations:

43x + 67y = – 24, 67x + 43y = 24

Answer 1

Given pair of linear equations is

43x + 67y = – 24   ......(i)

And 67x + 43y = 24   ......(ii)

On multiplying equation (i) by 43 and equation (ii) by 67 and then subtracting both of them, we get

(67)²x + 43 × 67y = 24 × 67
(43)²x + 43 × 67y = – 24 × 43
–             –                   +              
     {(67)² – (43)²}x = 24(67 + 43)

⇒ (67 + 43)(67 – 43)x = 24 × 110  ......[∵ (a² – b²) = (a – b)(a + b)]

⇒ 110 × 24x = 24 × 110

⇒ x = 1

Now, put the value of x in equation (i), we get

43 × 1 + 67y = – 24

⇒ 67y = – 24 – 43

⇒ 67y = – 67

⇒ y = – 1

Hence, the required values of x and y are 1 and –1, respectively.