Solve the following systems of simultaneous linear equations by the elimination method

15x - 14y = 117

14x - 15y = 115

Given,

15x - 14y = 117 …….(i)

14x - 15y = 115 …….(ii)

Multiplying eq. (i) by 14 and eq. (ii) by 15 we get,

210x - 196y = 1638 …….(iii)

210x - 225y = 1725 …….(iv)

Subtracting eq. (iii) from (iv) we get,

⇒ 210x - 225y - (210x - 196y) = 1725 - 1638

⇒ 210x - 210x - 225y + 196y = 87

⇒ -29y = 87

⇒ y = -3.

Substituting value of y in eq. (ii) we get,

⇒ 14x - 15(-3) = 115

⇒ 14x + 45 = 115

⇒ 14x = 115 - 45

⇒ 14x = 70

⇒ x = 5.

Hence, x = 5 and y = -3.