Question

Solve this pair of linear Equations
$6 x + 3y = 6xy \\ \\ and \\ \\ 2x + 4y = 5xy$
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Answer 1

Answer:

SO   HARD

Step-by-step explanation:

Answer 2

Answer:

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

$\frac{m}{( - 30 - ( - 12))} = \frac{n}{( - 24 - ( - 15)) } = \frac{1}{(6 - 24)}$

$\frac{m}{ - 18} = \frac{n}{ - 9} = \frac{1}{ - 18}$

m = 1

$\frac{n}{9} = \frac{1}{ - 18}$

$n = \frac{1}{2}$

$m = 1 \: and \: n = \frac{1}{2}$

$m = \frac{1}{x} = 1 \: and \: n = \frac{1}{y} = \frac{1}{2}$

x = 1 and y = 2

Hence, x = 1 and y = 2