How do you solve the following linear system: #x - 3y = 4x - 13 , y = 1/2x - 3/2 #?

1 Answer
Feb 26, 2017

Answer:

#x=3.89" , "y=0.45#

Explanation:

#x-3y=4x-13" (1)"#

#color(red)(y)=1/2 x-3/2" (2)"#

#"rearrange the equation (1) above"#

#x-4x=3y-13#

#-3x=3y-13#

#"divide both sides by 3"#

#(-cancel(3)x)/cancel(3)=(3y-13)/3#

#-x=(cancel(3)y)/cancel(3)-13/3#

#-x=y-13/3#

#color(red)(y)=-x+13/3" (3)"#

#"the equations (3) and (2) are equal"#

#"we can write as ;"#

#1/2x-3/2=-x+13/3#

#1/2x+x=13/3+3/2#

#x/2+color(green)(2/2) x=color(green)(2/2)*13/3+color(green)(3/3)3/2#

#(3x)/2=26/6+9/6#

#(3x)/2=35/6#

#"if "a/b=c/d" then "a*d=b*c#

#3x*6=2*35#

#18x=70#

#x=70/18#

#x=3.89#

#"use (2)"#

#y=1/2x-3/2#

#y=1/2*3.89-3/2#

#y=(3.89-3)/2#

#y=(0.89)/2#

#y=0.45#