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

1 Answer
Alan P.
Jun 22, 2016

#(x,y)=color(green)(""(0,2/3))#

Explanation:

Given:
[1]#color(white)("XXX")2x+3y=2#
[2]#color(white)("XXX")x+6y=4#

[1]#xx 2#
#color(white)("XXX")#[3]#color(white)("XXX")4x+6y=4#

[3]# - # [2]
#color(white)("XXX")#[4]#color(white)("XXX")3x=0#

[4]#div 3#
#color(white)("XXX")#[5]#color(white)("XXX")x=0#

Substituting (from [5]) #0# for #x# in [2]
#color(white)("XXX")#[6]#color(white)("XXX")0+6y=4

[6]#div 6#
#color(white)("XXX")#[7]#color(white)("XXX")y=2/3#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For verification purposes, you should check this result by substituting
#x=0# and #y=2/3# back into equation [1].

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