solve the system of equations

Question

r-3s+t = 4   

3r-6s+9t =5

4r-9s+10t =9.

Answer 1

Elimination method :

Given equations are r - 3 s + t = 4  ---> (1)

3 r - 6 s + 9 t  = 5 ------> (2)

4 r - 9 s + 10 t = 9 -----> (3)

Multiply each side by - 3 in eq ( 1)

We get the equation - 3 r +9 s - 3 t = - 12 ---------> ( 4 )

To eliminate the r  value add  (2 )&(4).

3 r - 6 s + 9 t  = 5

- 3 r + 9 s - 3 t = - 12

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3 s + 6 t = - 7  ----------> (5)

Multiply each side by - 4  in eq (2 )

We get the equation - 12 r + 24 s - 36 t = - 20 --------> (6)

Multiply each side by 3 in eq (3)

We get the equation 12 r - 27 s +30 t =  27--------> ( 7 )

To eliminate the r  value add (6)&(7).

- 12 r +24 s - 36 t = - 20

12 r - 27 s +30 t =  27

_________________

- 3 s - 6 t = 7 --------------> (8)

To eliminate the s and t  values  add (5)&(8).

3 s + 6 t = - 7

- 3 s - 6 t = 7

___________

0 - 0  = 0

0 = 0

The above statement is true.

So the system of equations have many solutions.