Question

Solve the following systems of equations:
1/ 2(x + 2y) + 5/ 3(3x – 2y) = –3/2
5/ 4(x + 2y) – 4/ 5(3x – 2y) = 73/60.

Answer 1

Solve the following systems of equations:

1/ 2(x + 2y) + 5/ 3(3x – 2y) = –3/2

5/ 4(x + 2y) – 4/ 5(3x – 2y) = 73/60.

x = 1/2 and y = 5/4

Given,

1/ 2(x + 2y) + 5/ 3(3x – 2y) = –3/2

5/ 4(x + 2y) – 4/ 5(3x – 2y) = 73/60.

Let 1/(x+2y) = u and (3x-2y) = v

Now, we have,

u/2 + 5v/3 = -3/2  ...........(1)

5u/4 - 4v/5 = 73/60 ..........(2)

Solving equations (1) and (2), we get,

u = 1/3 and v = -1

Therefore, we have  

1/(x+2y) = 1/3

⇒ x+2y = 3 ...........(3)

1/(3x-2y) = -1

⇒ 3x-2y = -1 ............(4)

x = 1/2 and y = 5/4

Hence the required values.