Question

152x - 378y = -74 , -378x + 152y = -600 find x and y​

Answer 1

$152x - 378y = - 74 \: \: \: \: \: ...(1) \\ - 378x + 152y = - 600 \: \: \: \: \: ...(2) \\divide \: (1) \: and \: (2) \: by \: 2 \\ \\ 76x - 189y = - 37 \: \: \: \: \: ...(3) \\ - 189x + 76y = - 300 \: \: \: \: \: ...(4)$

Multiply (3) by 76 and (4) by 189

$5776x - 14364y = - 2812 \: \: \: \: \: ...(5) \\ - 35721x + 14364y = - 56700 \: \: \: \: \: ...(6)$

Add (5) and (6)

$5776x - 14364y = - 2812 \\ - 35721x + 14364y = - 56700 \\ - - - - - - - - - - - - - \\ - 29945x = - 59512 \\ x = \frac{59512}{29945}$

From (3)

$76 \times \frac{59512}{29945} - 189y = - 37 \\ 189y = \frac{76 \times 59512}{29945} + 37 \\ y = \frac{4522912 + 37 \times 29945}{29945 \times 189} \\ y = \frac{4522912 + 1107965}{29945 \times 189} \\ y = \frac{5630877}{29945 \times 189} \\ y = \frac{29793}{29945}$