How do you solve the linear equation x+3y=2 and -x+y=1 using the substitution method and are they dependent, independent, or inconsistent?

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Answer 1 · 2017-10-22T22:28:19

#x = -(1/4), y = (3/4)#
They are dependent and consistent.

#x + 3y = 2#
#x = 2 - 3y color(white)(aaa) Eqn (2)

#-x + y = 1 color (white)(aaa)# Eqn (1),

Substituting value of “x “ in Eqn (1),

#-(2-3y) + y = 1#

#3y + y = 3#
#4y = 3, or y = 3/4#

Substituting value of “y” in Eqn (1),

#-x + (3/4) = 1#
#-x = 1/4, or x = -1/4#

Verification :
Substituting value of “y” in Eqn (2),
#x = 2 - 3y = 2 - 3(3/4) = 2 - 2(1/4) = -(1/4)#