How do you solve the following linear system: # x + 2y = 13, 3x – y = 4 #?

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Answer 1 · 2016-02-21T10:55:44

#color(blue)(x=3, y=5)#

we can use,

-#color(blue)(Substitution Method)#

Solving,

#color(red)(x+2y=13)#
as equation(1)

#color(red)(3x-y=4)#
as equation(2)

first we must get the value of #x# in equation(1), using algebraic techniques (isolating the variable #x#), we get:

#color(red)(x = 13-2y)#
as equation(3)

substitute equation(3) to equation(2) to eliminate #x#,

#3(13-2y)-y=4#

#39-6y-y=4# (Combine like terms to simplify)

#39-7y=4#

#-7y = 4 - 39#

#-7y = -35#

#y = (-35)/-7#

#color(blue)(y = 5)#

substitute #y# to either equation(1) or equation(2) to get the final value of variable #x#

Substituting #y# to Equation(1),

#x+2y=13#

#x+2(5)=13#

#x+10=13#

#x=13-10#

#color(blue)(x=3)#