Use the substitution and to rewrite the equations in the system in terms of the variables and. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y.

-3/x+4/y=11

1/x-2/y=-5

x = - 1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = - 5

Can be written as

-3u + 4v = 11 ... (1)

u - 2v = - 5 ... (2)

From (2)

u = 2v - 5 ... (3)

Substituting (3) into (1)

-3 (2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = - 4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2 (2) - 5

= 4 - 5

= - 1

That is

u = - 1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = - 1

=> x = - 1

And

1/y = 2

=> y = 1/2

Therefore

x = - 1 and y = 1/2