How do you solve the following system?: # -x+5y=7 , x=-2y+1 #

1 Answer
Nov 14, 2015

Answer:

Use linear combination or substitution.

Explanation:

Add the two equations together.
#-x+5y=7#
#+(x+2y=1)#
#color(red)(0x+7y=8)#
Therefore, #7y=8# and #y=8/7#. From here, plug #8/7# in for #y# in either equation and solve for #x#.

Another option would be substitution, since from the second equation you know that #x=-2y+1#, would be to replace #x# with #-2y+1# in the equation #-x+5y=7#.

This would give: #-(-2y+1)+5y=7#
#2y-1+5y=7#
#7y-1+7#
#7y=8#
Again, we see that #color(blue)(y=8/7)# and we would use that value to determine that #color(blue)(x=-9/7)#.