find values of r,s,t that produce the solution of (2,-3) pleas show how you got it...
-3x-5y=9
rx-sy=t
Solution
-3x-5y=9 -----eq.1
rx-sy=t ------eq.2
do r*eq1 + 3*eq.2
-3rx - 5ry = 9r
3rx - 3sy = 3t
--------------------
0 - y(5r + 3s) = 9r + 3t
==>
y = - (9r + 3t)/(5r + 3s)
given y = -3
==>
-3 = - (9r + 3t)/(5r + 3s)
==>
5r + 3s = 3r + t
=>
5r + 3s = t -------eq.3
and
do s*eq1 - 5*eq.2
-3sx - 5sy = 9s
5rx - 5sy = 5t
--------------------
- x(5r + 3s) + 0 = 9s - 5t
==>
x = - (9s - 5t)/(5r + 3s)
given x = 2
==>
2 = - (9s - 5t)/(5r + 3s)
==>
10r + 6s = -9s + 5t
=>
2r + 3s = t -------eq.4
from eq. 3 and 4 we get
5r + 3s = t
2r + 3s = t
-----------------
3r -0 = 0
=> r = 0
and
s = t/3
and
t = 3s
.
