Question

solve the following simultaneous equation
1. 49x- 57y = 172 ; 57x - 49y= 2
​

Answer 1

Given:

49x - 57y = 172 ——> 1

57x - 49y = 2 ——> 2

Adding 1 & 2,

106x - 106y = 174

53x - 53y = 87 ——> 3

Subtract 1 from 2, we get

8x + 8y = -170

x + y = -85 ——> 4

Multiply equation 4 with 53,

53x + 53y = -85*53 ——> 5

Adding 3 & 5,

106x = 87 - 85*53

106x = 87 - 4505

106x = - 4418

53x = - 2209

x = -2209/53

Subtract 3 from 5,

106y = -85*53 - 87

106y = - 4505 - 87

106y = -4592

y = - 2286/53

Therefore

x = -2209/53, y = - 2286/53 ——> Answer