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

x - 3y = 3x - 1 = 2x - y.

x - 3y = 3x - 1

⇒ 3x - x + 3y = 1

⇒ 2x + 3y = 1 …….(i)

3x - 1 = 2x - y

⇒ 3x - 2x + y = 1

⇒ x + y = 1 …….(ii)

Multiplying eq. (ii) by 2 we get,

2x + 2y = 2 ……..(iii)

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

⇒ 2x + 3y - (2x + 2y) = 1 - 2

⇒ 2x - 2x + 3y - 2y = -1

⇒ y = -1.

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

⇒ x + (-1) = 1

⇒ x = 1 + 1

⇒ x = 2.

Hence, x = 2 and y = -1.