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) About Me  (Show Source):
You can put this solution on YOUR website!
+x+=+13%2F5+
+y+=+1%2F5+
-------------
(1) +A%2A%2813%2F5%29+%2B+B%2A%281%2F5%29+=+15+
(2) +B%2A%28+13%2F5%29+-+A%2A%281%2F5%29+=+25+
------------------------------
(1) +13A+%2B+B+=+75+
(2) +-A+%2B+13B+=+125+
------------------------
Multiply both sides of (2) by +13+
and add the equations
(1) +13A+%2B+B+=+75+
(2) +-13A+%2B+169B+=+1625+
---------------------------
+170B+=+1700+
+B+=+10+
Plug this result back into (1) or (2)
(2) +-A+%2B+13B+=+125+
(2) +-A+%2B+13%2A10+=+125+
(2) +-A+%2B+130+=+125+
(2) +A+=+5+
------------------
check answers:
(1) +A%2A%2813%2F5%29+%2B+B%2A%281%2F5%29+=+15+
(1) +5%2A%2813%2F5%29+%2B+10%2A%281%2F5%29+=+15+
(1) +13+%2B+2+=+15+
OK
(2) +B%2A%28+13%2F5%29+-+A%2A%281%2F5%29+=+25+
(2) +10%2A%28+13%2F5%29+-+5%2A%281%2F5%29+=+25+
(2) +26+-+1+=+25+
(2) +25+=+25+
OK

Answer by ikleyn(52781) About Me  (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)  13%2F5 instead of  x  and  1%2F5  instead of y. Uoi will get

    A%2A%2813%2F5%29 + B%2A%281%2F5%29 = 15,     (1)

    B%2A%2813%2F5%29 - A%2A%281%2F5%29 = 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.