Question

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

Answer 1

The solution for the given system of equations is : x = 3, y = 2

• Given equations are :

x + (y / 2) = 4

=> (2x + y) / 2 = 4

=> 2x + y = 4 × 2

=> 2x + y = 8  -(i)

(x / 3) + 2y = 5

=> (x + 2y.3) / 3 = 5

=> (x + 6y) / 3 = 5

=> x + 6y = 5 × 3

=> x + 6y = 15  -(ii)

• Multiplying equation (ii) by 2, we get,

2 (x + 6y) = 2 × 15

=> 2x + 2.6y = 30

=> 2x + 12y = 30 -(iii)

• Subtracting equation (iii) from (i), we get,

(i) - (iii)

=> (2x - 2x) + (y - 12y) = 8 - 30

=> 0 + (- 11y) = - 22

=> - 11y = - 22

=> y = (- 22) / (- 11)

=> y = 2

• Now, putting the value of y in eq. (i), we get,

2x + 2 = 8

=> 2x = 8 - 2

=> 2x = 6

=> x = 6 / 2

=> x = 3

• ∴  The value of x = 3

The value of y = 2

Answer 2

x = 3 and y = 2

Step-by-step explanation:

The given systems of equations are:

x + $\dfrac{y}{2}$ = 4                      ............ (1)

and $\dfrac{x}{3}$ + 2y = 5           ............ (2)

To find, the values of x and y = ?

Multiply equation (1) by 4, we get

4(x + $\dfrac{y}{2}$ ) = 4 × 4

⇒ 4x + 2y = 16          ............ (3)

Subtracting (2) from (3), we get

4x + 2y - ($\dfrac{x}{3}$ + 2y ) = 16 - 5    

⇒ 4x + 2y - $\dfrac{x}{3}$ - 2y = 11

⇒ 4x - $\dfrac{x}{3}$ = 11

⇒ $\dfrac{11x}{3}$ = 11

⇒ x = 3

Put x = 3 in equation (3), we get

4(3) + 2y = 16

⇒ 2y = 16 - 12 = 4

⇒ y = 2

∴ x = 3 and y = 2