SOLUTION: The solution of the following linear system is (13/5 , 1/5). Solve for the values of A and B. Show your work. Ax+By=15 Bx-Ay=25 Thanks!

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Question 1037109: The solution of the following linear system is (13/5 , 1/5). Solve for the values of A and B. Show your work.
Ax+By=15
Bx-Ay=25
Thanks!
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!


-------------
(1)
(2)
------------------------------
(1)
(2)
------------------------
Multiply both sides of (2) by
and add the equations
(1)
(2)
---------------------------


Plug this result back into (1) or (2)
(2)
(2)
(2)
(2)
------------------
check answers:
(1)
(1)
(1)
OK
(2)
(2)
(2)
(2)
OK
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The solution of the following linear system is (13/5 , 1/5). Solve for the values of A and B. Show your work.
Ax+By=15
Bx-Ay=25
Thanks!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  Substitute (plug-in)   instead of  x  and    instead of y. Uoi will get

     +  = 15,     (1)

     -  = 25.     (2)

    They want you solve this system for A and B.


2.  Multiply the eqns (1) and (2) by 5 (both sides) to rid of denominators.
    Write the system in the canonical form. You will get

     13A +   B =  75,     (1')
      -A + 13B = 125.     (2')


3.  Now solve it. You can apply the substitution method by expressing A = 13b - 125 from (2') and substituting it into eqn (1).


From this point please complete the solution on your own.


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