Question

solve x and y :- 2/x+y + 3/x-y=1 , 8/x+y - 7/x-y = 5/6​ explain step by step

Answer 1

Answer:

x=3 and y=2

Step-by-step explanation:

Given Equation:

\dfrac{5}{x+y}-\dfrac{2}{x-y}=-1

\dfrac{15}{x+y}+\dfrac{7}{x-y}=10

\dfrac{1}{x+y}=u

\dfrac{1}{x-y}=v

Reducible linear equation

5u-2v=-1

15u+7v=10

Using elimination method to solve for u and v

We will make coefficient of u same in both equation. So, we multiply first equation by 3 and we get

15u-6v=-3

15u+7v=10

Subtract (2) - (1)

7v+6v=10+3

13v=13

v=1

Substitute v into 15u+7v=10

15u+7(1)=10[/tex[</p><p>$u=\dfrac{1}{5}</p><p>\dfrac{1}{x+y}=\dfrac{1}{5}\Rightarrow x+y=5</p><p>\dfrac{1}{x-y}=1\Rightarrow x-y=1</p><p>Add both equation and eliminate y</p><p>2x=6</p><p>x=3</p><p>Substitute x=3 into x+y=5</p><p>3+y=5</p><p>y=2</p><p>Hence, x=3 and y=2 is solution of system of equation.</p><p>[tex]< marquee > (hopeithelp)$