Question

Solve 6x+3y=6xy and 2x+4y=5xy by reducing them to pair of linear equation

Answer 1

$two \: equations \: are \: as \: follows - \\ 6x + 3y = 6xy - - - (1) \\ 2x + 4y = 5xy - - - (2) \\ \\ multiply \: eq.(1) \: by \: 5 \: and \: eq.(2) \: by \: 6 \\ 30x + 15y = 30xy - - (3)\\ 12x + 24y = 30xy - - (4) \\ eq.(3) \: and \: (4) \: are \: equal \: so \\ \\ 30x + 15y = 12x + 24y \\ 18x = 9y \\ y = 2x \\ \\ if \\ y = 0 \: then \: x = 0 \\ y = 1 \: then \: x = 2 \\ y = 3 \: then \: x = 6$
so for every value of x there is value of value of y and vice versa.

Answer 2

X= 1 and Y = 2

Step-by-step explanation:

Given equations: 6x + 3y = 6xy and 2x + 4y = 5xy

Consider the two given equations

There are two variables x and y in the given linear equation

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