How do solve the following linear system?: # x+2y=1 , -2x -8y = 4 #?

2 Answers
Feb 1, 2017

Answer:

#x=4# and #y=-3/2# or #-1 1/2#

Explanation:

#x+2y=1#
#-2x-8y=4#

Reduce the second equation by dividing all terms by #2#.

#-2x-8y=4#

#-x-4y=2#

Multiply all terms by #-1#.

#x+4y=-2#

Separate #4y# into two.

#x+2y+2y=-2#

In this equation, substitute #(x+2y)# with #color(red)(1)#, the value from the first equation.

#x+2y+2y=-2#

#color(red)(1)+2y=-2#

Subtract #1# from both sides.

#2y=-3#

Divide both sides by #2#.

#y=-3/2=-1 1/2#

In the first equation, substitute #y# with #color(blue)(-3/2)#.

#x+2y=1#

#x+2color(blue)((-3/2))=1#

Open the brackets and simplify.

#x-3=1#

Add #3# to both sides.

#x=4#

Feb 1, 2017

Answer:

#y=-1 1/2, x=4#

Explanation:

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

#-2x-8y=4#---------(2)

#2x+4y=2# #(1) xx 2 # ---------(3)

#-4y=6#--------(2)+(3)

#4y=-6#

#y=-6/4#

#y=-1 1/2#

Substitute #y=-6/4# in ----------1

#x+2(-6/4)=1#

#x-12/4=1#

#x-3=1#

#x=1+3#

#x=4#
Substitute #y= -6/4,x=4 in------1

#4+2(-6/4)=1#

#4-12/4=1#

multiply both sides by 4
#16-12=4#

#4=4#