Solve the following system of equations:x + y/2 = 4; 2y + x/3 = 5

1.	Solve the following system of equations:x + y/2 = 4; 2y + x/3 = 5
Answer» The given pair of equations are: x + y/2 = 4 …………(i) 2y + x/3 = 5…………(ii) From (i) we get, x + y/2 = 4 ⇒ 2x + y = 8 [After taking LCM] ⇒ y = 8 – 2x …..(iv) From (ii) we get, x + 6y = 15 …………(iii) [After taking LCM] Substituting y in (iii), we get x + 6(8 – 2x) = 15 ⇒ x + 48 – 12x = 15 ⇒ -11x = 15 – 48 ⇒ -11x = -33 ⇒ x = 3 Putting x = 3 in (iv), we get y = 8 – (2 x 3) ∴ y = 8 – 6 = 2 Hence, the solution of the given system of equation are x = 3 and y = 2 respectively.

Answer»

The given pair of equations are:

x + y/2 = 4 …………(i)

2y + x/3 = 5…………(ii)

From (i) we get,

x + y/2 = 4

⇒ 2x + y = 8 [After taking LCM]

⇒ y = 8 – 2x …..(iv)

From (ii) we get,

x + 6y = 15 …………(iii) [After taking LCM]

Substituting y in (iii), we get

x + 6(8 – 2x) = 15

⇒ x + 48 – 12x = 15

⇒ -11x = 15 – 48

⇒ -11x = -33

⇒ x = 3

Putting x = 3 in (iv), we get

y = 8 – (2 x 3)

∴ y = 8 – 6 = 2

Hence, the solution of the given system of equation are x = 3 and y = 2 respectively.

Discussion