How do you solve the system of equations #Ax+3By=-1# and #-5Ax+By=-19#, if #x=3# and #y=1#?

1 Answer
Jim G.
Nov 15, 2017

#A=7/6" and "B=-3/2#

Explanation:

#"given the solution to the equations "(3,1)#

#"then substitute these values into the equations "#
#"and solve for A and B"#

#rArr3A+3B=-1to(1)#

#rArr-15A+B=-19to(2)#

#"multiply equation "(1)" by 5"#

#rArr15A+15B=-5to(3)#

#"add equations "(2)+(3)" to eliminate A"#

#(-15A+15A)+(B+15B)=(-19-5)#

#rArr16B=-24#

#"divide both sides by 16"#

#(cancel(16) B)/cancel(16)=-24/16=-3/2#

#rArrB=-3/2#

#"substitute this value into equation "(1)#

#3A+3(-3/2)=-1#

#rArr3A=-1+9/2=7/2#

#"divide both sides by 3"#

#rArrA=7/6#

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