Question

Solve for X and Y, ​

Answer 1

Step-by-step explanation:

Lets put

$x + 2y = a \\ x - 2y = b$

we get

$\frac{6}{a} + \frac{5}{b} = - 3 \\ \frac{3}{a} + \frac{7}{b} = - 6$

By cross multiplying

6b+5a= -3ab. (1)

3b+7a= -6ab. (2)

multiply (1) by 2

we get

12b+10a=-6ab. (3)

subtract (2) from (3)

we get

3b= -a

put this in (2)

we get

a=3

b= -1

Now a= x+2y=3

b=x-2y= -1

we get

X=1

Y=1

Answer 2

$\boxed{ \rm\frac{6}{x + 2y} + \frac{5}{x - 2y} = \: \: - 3 } \bf\: \: \: \: \: \: \cdots(i)\\ \boxed{ \rm\frac{3}{x + 2y} + \frac{7}{x - 2y} = \: \: - 6} \bf\: \: \: \: \: \: \cdots(ii)$

Multiplying Equation (ii) by 2 & Equation (i) by 1, we get,

$\boxed{ \rm\frac{6}{x + 2y} + \frac{5}{x - 2y} = \: \: - 3 } \bf\: \: \: \: \: \: \cdots(iii)\\ \boxed{ \rm\frac{6}{x + 2y} + \frac{14}{x - 2y} = \: \: - 12} \bf\: \: \: \: \: \: \cdots(iv)$

Subtracting equation (iii) from (iv), we get,

$\to \tt \frac{14}{x - 2y} - \frac{5}{x - 2y} = - 12 + 3 \\ \\ \to \tt \frac{14 - 5}{x - 2y} = \: - 9 \\ \\ \to \tt \frac{9}{x - 2y} = - 9 \\ \\ \to \tt \frac{\cancel9}{x - 2y} = - \cancel9 \\ \\ \to \tt \frac{1}{x - 2y} = - 1 \\ \to \boxed{ \tt x - 2y = - 1} \bf\: \: \: \: \: \: \: \cdots(v)$

Putting equation (v) in equation (i), we get,

$\to \tt \frac{6}{x + 2y} + \frac{5}{( - 1)} = - 3 \\ \\ \to \tt \frac{6}{x + 2y} = - 3 - ( - 5) \\ \\ \to \tt \frac{6}{x + 2y} = - 3 + 5 \\ \\ \to \tt \frac{6}{x + 2y} = 2 \\ \\\to \tt x + 2y = \frac{6}{2} \\ \\ \to \boxed{ \tt x + 2y = 3} \bf\: \: \: \: \: \: \: \: \cdots(vi)$

Adding equation (v) and (vi), we get,

→ x + x - 2y + 2y = -1 + 3

→ 2x = 2

→ x = 1

Putting value of x in equation (vi), we get,

x + 2y = 3

→ y = (3 - x)/2

→ y = (3 - 1)/2

→ y = 2/2 = 1

Thus,

$\boxed{ \large \sf{Value \: \: of \: \: x \: \: \red{\&} \: \: y \: {\orange{=}} \: \green1}}$