Question

solve for x and y 15/x+y - 5/x-y=-2 10/x+y+2/x-y=4 ​

Answer 1

Step-by-step explanation:

${:}\longrightarrow$

$\frac{15}{x + y} - \frac{5}{ x- y} = - 2 \\ = > \frac{15(x - y) - 5(x + y)}{(x + y)(x - y)} = - 2 \\ = > \frac{15x - 15y - 5x - 5y}{ {x}^{2} - {y}^{2} } = - 2 \\ = > \frac{15x - 5x - 15y - 5y}{ {x}^{2} - {y}^{2} } \\ = > \frac{10x - 10y}{ {x}^{2} - {y}^{2} } = - 2 \\ = > 10x - 10y = - 2( {x}^{2} - {y}^{2} ) \\ = > 10(x - y) = - 2(x - y)(x + y) \\ = > 2(x + y) = 10 \\ = > 2x + 2y = 10 \\ = > 2(x + y) = 10 \\ = > x + y = \frac{10}{2} = 5$

Answer 2

x+y

15

−

x−y

5

=−2

=>

(x+y)(x−y)

15(x−y)−5(x+y)

=−2

=>

x

2

−y

2

15x−15y−5x−5y

=−2

=>

x

2

−y

2

15x−5x−15y−5y

=>

x

2

−y

2

10x−10y

=−2

=>10x−10y=−2(x

2

−y

2

)

=>10(x−y)=−2(x−y)(x+y)

=>2(x+y)=10

=>2x+2y=10

=>2(x+y)=10

=>x+y=

2

10

=5