How do you solve the following system of equations?: #4x – y = 14 , -3x + 3y=10#?

1 Answer
Alan P.
Dec 19, 2015

#(x,y)=(52/9,82/9)#
#color(white)("XXXXXXXXXXXX")#(not all answers are pretty)

Explanation:

Solving by Substitution
Given
[1]#color(white)("XXX")4x-y=14#
[2]#color(white)("XXX")-3x+3y=10#

Re-write [1] as
[3]#color(white)("XXX")y= 4x-14#

Substitute #4x-14# (from [3]) for #y# in [2]
[4]#color(white)("XXX")-3x+3(4x-14)=10#

Simplify
[5]#color(white)("XXX")9x-42=10#

[6]#color(white)("XXX")9x=52#

[7]#color(white)("XXX")x=52/9#

Substituting #(52/9)# for #x# in [1]
[8]#color(white)("XXX")4xx(52/9)-y=14#

[9]#color(white)("XXX")y= 208/9-14 = (208-126)/9 = 82/9#

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