Question

Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252

Answer 1

49x – 57y = 172   ...(I)

57x – 49y = 252   ...(II)

Adding equations (I) and (II)

(49x + 57x) + (–57y – 49y) = 172 + 252

106x + (–106y) = 424

106(x – y) = 424

(x – y) = `424/106`

∴ x – y = 4   ...(III)

Subtracting (II) from (I) we have

(57x – 49x) + [–49y – (–57y)] = 252 – 172

8x + (–49y + 57y) = 80

8x + 8y = 80

8(x + y) = 80

x + y = `80/8`

x + y = 10   ...(IV)

Adding (III) and (IV)

x + x – y + y = 4 + 10

2x = 14

x = 7

Putting the value of x = 7 in (IV) we get

x + y = 10

7 + y = 10

y = 10 – 7

y = 3

Thus, (x, y) = (7, 3)