Solve for X & Y x/2+y/3=2, x+2y=8​

Given :-

x/2 + y/3 = 2 .........eq( 1 )

x + 2y = 8 ................eq( 2 )

Solution :-

Take equation 1

x/ 2 + y/3 = 2

Solve by taking LCM

3x + 2y / 6 = 2

3x + 2y = 2*6

3x = 12 - 2y

x = (12 - 2y)/3 ...........eq( 3 )

Take eq( 2)

x + 2y = 8

Subsitute eq (3) in eq( 2)

(12 - 2y)/3 + 2y = 8

By taking LCM

12 - 2y + 6y /3 = 8

12 - 2y + 6y = 8 * 3

12 + 4y = 24

4y = 24 - 12

4y = 12

y = 12/4

y = 3 ...........eq( 4)

Subsitute eq(4) in eq( 1)

x/2 + y/3 = 2

Put the required value of y in the equation 4

x/ 2 + 3/3 = 2

x/2 + 1 = 2

By taking LCM

x + 2 / 2 = 2

x + 2 = 2*2

x + 2 = 4

x = 4 - 2

x = 2

Hence, The value of x is 2

The value of y is 3

Verification :-

2/2 + 3/3 = 2

1 + 1 = 2

2 = 2

LHS = RHS

2 + 2 * 3 = 8

2 + 6 = 8

8 = 8

LHS = RHS