How do you solve the following system of equations?: #13x+3y=16, 7x-5y=69#?

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Answer 1 · 2016-02-11T11:18:24

#x =287/86 ; y=-785 /86#

#13x+3y=16 # ----------(1)
#7x -5y =69 #----------(2)

Multiply #eq^n # (1) by 5 and #eq^n # (2) by 3 we get,

#65x+15y=80 # ----------(3)
#21x -15y =207 #----------(4)

Add the #eq^n # (3) and #eq^n # (4)

#[65x+15y=80] + [21x -15y =207] #

#65x+21x +15y-15y = 80+207#

#86x = 287#

#x =287/86#

Substitute in #eq^n (1)#

#13x+3y=16 #

#13(287/86)+3y=16 #

#3731/86 +3y =16#

#3y = 16-3731/86#

#3y = (1376-3731)/86#

#3y= -2355/86#

#y= -2355/(86xx3)#

#y=-785 /86#