How do solve the following linear system?: # x+2y=1 , 4 x+ 16y = 2 #?

1 Answer
Alan P.
Dec 8, 2015

#(x,y) = (3/2, -1/4)#

Explanation:

Given
[1]#color(white)("XXX")x+2y=1#
[2]#color(white)("XXX")4x+16y=2#

Multiply [1] by #4# to generate the same #x# coefficient as in [2]
[3]#color(white)("XXX")4x+8y=4#

Subtract [3] from [2]
[4]#color(white)("XXX")8y=-2#

Divide both sides of [4] by #8#
[5]#color(white)("XXX")y = -1/4#

Substitute #(-1/4)# for #y# in [2]
[6]#color(white)("XXX")4x+16*(-1/4)=2#

Simplify:
[7]#color(white)("XXX")4x-4 = 2#

Add #4# to both sides
[8]#color(white)("XXX")4x = 6#

Divide both sides of [8] by #4#
[9]#color(white)("XXX")x=3/2#

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