Question

solve: 2x + 3y =5xy and 4x + 5y = 7xy​

Answer 1

Answer:

your answer attached in the photo

Answer 2

$\large\underline\pink{Given:-}$

• 2x + 3y = 5xy and 4x + 5y = 7xy

$\large\underline\pink{To find:-}$

• Fine the value of x and y ....?

$\large\underline\pink{Solutions:-}$

2x + 3y = 5xy ______(i)

4x + 5y = 7xy ______(ii)

multiplying Eq. (i) by 2 and Eq. (ii) by (1), we get.

4x + 6y = 10xy ________(iii)

4x + 5y = 7xy _________(iv)

Subtracting Eq. (iii) from Eq. (iv).

${4x} \: + \: {6y} \: \: = \: \: {10xy} \\ {4x} \: + \: {5y} \: \: = \: \: {7xy} \\ \underline{- \: \: \: \: \: \: \: \: \: - \: \: \: \: = \: \: \: \: \: - \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: {y} \: \: \: \: \: = \: \: \: {3xy}$

$\: \: \: \: \: \leadsto \: \: x \: \: = \: \: \frac{1}{3}$

$\: \: \: \: \: \leadsto \: \: {1}$

Now, putting the value x in Eq. (i)

2x + 3y = 5xy

2(1/3) + 3y = 5 × (1/3) × y

2/3 + 3y = 5y/3

9y - 5y = -2

4y = -2

y = -1/2

hence, the value of x is 1/3 and y is -1/2.