In the system let p1x and q1y Substitute solve for p and q a

In the system, let p=1/x and q=1/y.
Substitute, solve for p and q, and then find x and y.

3/x+4/y=8/5
5/x-2/y=1/2
The solution set is
Type an ordered pair.

Solution

p = 1/x

q = 1/y

we have

3/x + 4/y = 8/5                    => 3 * (1/x) + 4 * (1/y) = 8/5

5/x - 2/y = 1/2                     => 5 * (1/x) - 2 *(1/y) = 1/2

3p + 4q = 8/5             (1)            //   p = 1/x

5p - 2q = 1/2               (2)            //   q = 1/y

multiply (2) by \"2\" and add it to (1)

10p - 4q = 1

3p + 4q = 8/5

+     +        +

13p = 1 + 8/5

13p = 13/5

p = 1/5

plug p = 1/5 in (1), we get

3 * (1/5) + 4q = 8/5

3/5 + 4q = 8/5

4q = 8/5 - 3/5

4q = 5/5

4q = 1

q = 1/4

now

p = 1/x

1/5 = 1/x

multiply by \"5\" on both sides

5/5 = 5/x

1 = 5/x

x = 5

q = 1/y

1/4 = 1/y

4/4 = 4/y

1 = 4/y

y = 4

so

x = 5   and y = 4