Question

solve 22/x+y+15/x-y=5and 55/x+y+45/x-y=14

Answer 1

Answer:

(x+y)²=7.4 and (x+y)²=7.14

Answer 2

Answer:

The solution for 22/x+y+15/x-y=5and 55/x+y+45/x-y=14 is:

y = 3 and x = 8

Explanation:

Let:

x + y = m and x - y = n

Doing the substitution we have:

22/m + 15/n = 5......................i)

55/m + 45/n = 14....................ii)

rewriting the equations we have:

22n + 15m = 5mn..................iii)

55n + 45m = 14mn..............iv)

Let's eliminate m by multiplying iii by 3 and subtracting the two equations.

11n = mn

Divide all through by n to get m:

m = 11

Substitute m in iii to get:

22n + 165 = 55n

55n - 22n = 165

33n = 165

n = 5

Since we have the values of m and n, we have that:

x + y = 11.........................v)

x - y = 5........................vi)

Let's eliminate y by adding the two equations:

2x = 16

x = 16/2 = 8

8 + y = 11

y = 11 - 8

y = 3