How do you solve the following system?: # -29x +53y =-26 , 45x +26y = -1#

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Answer 1 · 2016-02-28T06:55:21

#x= 623/3139# & #y=-1199/3139#

#-29x+53y=-26#-----------------------------------------(1)
#45x+26y = -1# ------------------------------------------(2)

Comparing with #a_1+b_1=c_1# and #a_2+b_2=c_2#

We get,
#a_1 =-29 ; b_1=53 ; c_1=-26#
#a_2=45; b_2=26= c_2 = -1#

#D =(a_1b_2)-(a_2b_1)#
#D= (-29xx26) - ( 45xx53)#
#D= (-754) - (2385)#
#D= -3139#

#D_x = (c_1b_2)-(c_2b_1)#
#D_x = (-26xx26)-(-1xx53)#
#D_x = (-676)-(-53)#
#D_x = -676+53#
#D_x = -623#

#D_y=(a_1c_2)-(a_2c_1)#
#D_y=(-29xx-1)-(45xx-26)#
#D_y=(29)-(-1170)#
#D_y=29+1170#
#D_y=1199#

By Cramer's Rule

#x= D_x/D#

#x=(-623)/-3139#

#x= 623/3139#

#y=D_y/D#

#y=1199/-3139#

#y=-1199/3139#