Question

6x+3y= 6xy
2x +4y= 5xy​

Answer 1

Answer: x = 1 and y = 2

Consider the two given equations

6x + 3y = 6xy…………………………(1)

2x + 4y = 5xy…………………………(2)

Divide equation (1) and (2) by xy we get

6/y + 3/x = 6………………………….(3)

2/y + 4/x = 5………………………….(4)

Let us consider from equation (3)

1/x = m and 1/y = n

=> 6n +3m = 6

=> 3m + 6n – 6 = 0…………………….(5)

Let us consider from equation (4)

=> 2/y + 4/x = 5

=> 2n +4m = 5

=> 4m + 2n – 5 = 0……………………..(6)

3m + 6n – 6 = 0

4m + 2n – 5 = 0

By cross-multiplication method, we get

m/(-30 –(-12)) = n/(-24-(-15)) = 1/(6-24)

m/-18 = n/-9 = 1/-18

m/-18 = 1/-18

m = 1

n/-9 = 1/-18

n = 1/2

m = 1 and n = 1/2

m = 1/x = 1 and n = 1/y = 1/2

x = 1 and y = 2

Hence, x = 1 and y = 2

Answer 2

6x + 3y = 6xy _(1) 2x + 4y = 5xy _(2)

• Divide equation (1) and (2) by xy we get

6/y + 3/x = 6 _(3) 2/y + 4/x = 5 _(4)

• Let 1/x = m and 1/y = n

6n + 3m = 6 _(5) 2n + 4m = 5 _(6)

• Multiply eqn. (5) by 2 & eqn. (6) by 6

12n + 6m = 12 12n + 24m = 30

• Solving above eqn. , we get,

m = 1 and n = 1/2

m = 1/x = 1 and n = 1/y = 1/2

x = 1 and y = 2

Hence, x = 1 and y = 2