Question

Solve the following systems of equations:
5/(x + y) – 2/(x – y) = –1
15/(x + y) + 7/(x – y) = 10

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>[tex]u=\dfrac{1}{5}

\dfrac{1}{x+y}=\dfrac{1}{5}\Rightarrow x+y=5

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

Add both equation and eliminate y

2x=6

x=3

Substitute x=3 into x+y=5

3+y=5

y=2

Hence, x=3 and