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

2x = 5y + 4

3x - 2y + 16 = 0

Given,

2x = 5y + 4 or 2x - 5y - 4 = 0 ……..(i)

3x - 2y + 16 = 0 ……(ii)

Multiplying eq. (i) by 3 and eq. (ii) by 2 we get,

6x - 15y - 12 = 0 …….(iii)

6x - 4y + 32 = 0 …….(iv)

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

⇒ 6x - 4y + 32 - (6x - 15y - 12) = 0

⇒ 6x - 6x - 4y + 15y + 32 + 12 = 0

⇒ 11y + 44 = 0

⇒ 11y = -44

⇒ y = -4.

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

⇒ 3x - 2(-4) + 16 = 0

⇒ 3x + 8 + 16 = 0

⇒ 3x + 24 = 0

⇒ 3x = -24

⇒ x = -8.

Hence, x = -8 and y = -4.