Question

6x+3y/xy=6;2x+4y/xy=5​

Answer 1

Step-by-step explanation:

Given:-

6x+3y/xy=6;

2x+4y/xy=5

To find:-

Solve the following equations?

Solution:-

Given pair of linear equations are:

6x+3y/xy=6

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

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

=> 3[(2/y) +(1/x)] = 6

=> (2/y) +(1/x) = 6/3

=> (2/y) +(1/x) = 2

(1/x) +(2/y) = 2---------(1)

2x+4y/xy=5

=> (2x/xy) +(4y/xy) = 5

=> (2/y) +(4/x) = 5

(4/x) + (2/y) = 5 --------(2)

Put 1/x = a and 2/y = b then

a+b = 2--------(3)

4a+b = 5 ------(4)

On subtracting (3) from (4)

4a + b = 5

a + b = 2

(-)

__________

3a + 0 = 3

___________

=> 3a = 3

=> a = 3/3

=> a = 1

On Substituting the value of x in (3)

1+b = 2

=> b = 2-1

=> b = 1

Therefore,a = 1/x = 1

=> x = 1

and b = 2/y = 1

=> y = 2

Therefore,x = 1 and y = 2

Answer:-

The solution for the given problem is (1,2)

Check:-

If x = 1 and y = 2

LHS of first equation

[6(1)+3(2)]/(1×2)

=> (6+6)/2

=> 12/2

=> 6

and

[2(1)+4(2)]/(1×2)

=> (2+8)/2

=> 10/2

=>5

Verified the given relations

Used Method:-

• Elimination method