Question

solve the following system of equations
●8v - 3u =5uv
●6v-5u = -2uv...​

Answer 1

Answer:

8v - 3u = 5uv

8v/uv - 3u/uv = 5

8/u - 3/v = 5 ----------------- Equation 1

6v - 5u = -2uv

6v/uv - 5u/uv = -2

6/u - 5/v = -2 ----------------Equation 2

Let 1/u =a and 1/v = b

8a - 3b = 5 ×5

6a - 5b = -2 ×3

40a -15b = 25 --------------Equation 3

18a - 15b = -6 ---------------Equation 4

Subtracting Equation 3 and Equation 4

40a - 15b = 25

- 18a - 15b = -6

+ +

----------------------------

22a = 31

----------------------------

a = 31/22

putting value of a in Equation 4

18 × 31/22 - 15b = -6

9 × 31/11 - 15b = -6

279/11 - 15b = -6

-15b = -6 - 279/11

-15b = -66/11 - 279/11

-15b = -345/11

b = -345/11 ×1/-15

b = 23/11

Therefore,

1/u = a

1/u = 31/22

u = 22/31

1/v = b

1/v = 23/11

v = 11/23