Question

Solve the following system of equations algebraically:

73x − 37y = 109

37x − 73y = 1

Answer 1

73x − 37y = 109    ...(1)

37x − 73y = 1    ...(2)

From equation (2)

37x = 1 + 73у

x = `(1 + 73y)/37`    ...(3)

Substitute the value of x in equation (1).

`73((1 + 73y)/37) - 37y = 109`

`(73 + 5329y)/37 - (37y)/1 = 109`

`(73 + 5329y - 1369y)/37 = 109`

⇒ 73 + 3960y = 109 × 37

⇒ 73 + 3960y = 4033

⇒ 3960y = 4033 − 73

3960y = 3960

y = `3960/3960`

y = 1

Substitute the value of y in equation (3).

x = `(1 + 73(1))/37`

x = `74/37`

x = 2