How do you solve the following system?: #-12x -15y =3, x -16y = -4#

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Answer 1 · 2016-08-01T19:48:26

#x=-1296/2484#
#y=45/207#

#-12x-15y=3" ; "(1)#
#"rearrange the equation (1)"#

#color(green)(-12x)=3+15y" ; "(2)#

#x-16y=-4" ; "(3)#

#"let us expand the equation (3) by -12"#

#color(red)(-12)*(x-16y)=color(red)(-12)(-4)#

#-12x+192y=48#

#color(green)(-12x)=48-192y" ; "(4)#

#"the left side of the equation (2) and (4) are equal"#

#3+15y=48-192y#

#15y+192y=48-3#

#207y=45#

#y=45/207#

#"now use (1) or (3)"#

#-12x-15(45/207)=3#

#-12x-675/207=3#

#-12x=3+675/207#

#-12x=(621+675)/207#

#-12x=1296/207#

#-x=1296/(12*207)#

#x=-1296/2484#