Question

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

x+y

5

−

x−y

2

=−1

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

x+y

15

+

x−y

7

=10

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

x+y

1

=u

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

x−y

1

=v

Reducible linear equation

5u-2v=-15u−2v=−1

15u+7v=1015u+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[ [tex]u=\dfrac{1}{5}15u+7(1)=10[/tex[[tex]u=

5

1

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

x+y

1

=

5

1

⇒x+y=5

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

x−y

1

=1⇒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 y=2 is solution of system of equation.