How do you solve the following linear system: # 8x - 7y = -3 , x = 2y - 1 #?

1 Answer
Jim G.
Mar 31, 2018

#(x,y)to(1/9,5/9)#

Explanation:

#8x-7y=-3to(1)#

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

#"equation "(2)" expresses x in terms of y"#

#"substitute "x=2y-1" into equation "(1)#

#8(2y-1)-7y=-3larrcolor(blue)"distribute"#

#rArr16y-8-7y=-3larrcolor(blue)"simplify left side"#

#rArr9y-8=-3#

#"add 8 to both sides"#

#9ycancel(-8)cancel(+8)=-3+8#

#rArr9y=5#

#"divide both sides by 9"#

#(cancel(9) y)/cancel(9)=5/9#

#rArry=5/9#

#"substitute "y=5/9" into equation "(2)#

#rArrx=10/9-9/9=1/9#

#"solution is "(x,y)to(1/9,5/9)#

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