Question

Solve the following systems of equations r=2(s-t) ; 2t=3(s-r) ; r+t=2s-3.

Answer 1

r = 2

s = 4

t = 3

Explanation:

Given:

r = 2(s - t)

or

r = 2s - 2t .............(1)

2t = 3( s - r) ...............(2)

r + t = 2s - 3 .............(3)

substituting 1 in 3, we get

2(s - t) + t = 2s - 3

or

2s - 2t + t = 2s - 3

or

-t = 2s - 3 - 2s

or

t = 3

substituting t in 3 we get

r + 3 = 2s - 3

or

r = 2s - 6

substituting r and t in 2, we get

2 × 3 = 3( s - (2s - 6))

or

2 = s - 2s - 6

or

- 4 = -s

or

s = 4

substituting value of s and t in 1 , we get

r = 2 ( 4 - 3 )

or

r = 2

thus,

r = 2

s = 4

t = 3