How do you solve the following linear system: #x=6-4y , 2x-3y=1 #?

1 Answer
Jim G.
Mar 22, 2018

#(x,y)to(2,1)#

Explanation:

#x=6-4yto(1)#

#2x-3y=1to(2)#

#"equation "(1)" expresses x in terms of y"#

#color(blue)"Substitute "x=6-4y" into equation "(2)#

#2(6-4y)-3y=1larrcolor(blue)"distribute"#

#12-8y-3y=1larrcolor(blue)"collect like terms"#

#12-11y=1#

#"subtract 12 from both sides"#

#cancel(12)cancel(-12)-11y=1-12#

#rArr-11y=-11#

#"divide both sides by "-11#

#(cancel(-11) y)/cancel(-11)=(-11)/(-11)#

#rArry=1#

#"substitute "y=1" into equation "(1)#

#rArrx=6-4=2#

#rArr"solution is "(2,1)#

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