We will use elimination to solve this linear system.
Firstly we need to get same numbers but opposite sign from that same number.
In #x + 6y=28# /#* (-6)# (multiply the first equation with #-6#)
#6x-5y=-1#
We get,
#color(blue)(-6x)-36y=-168# ------- #color (red) (equation 1#
#color(blue)(6x)-5y=-1# ------ #color(blue)(equation 2)#
You can see that #-6x# and #6x# are opposites so we cancel them but firstly write the following,
#cancel(-6x)-36y+cancel(6x)-5y=-168-1#
#-41y=-169# From here
#y=-169/-41#
#y=169/41#
It's now
#-6x-36y=-168# ------- #color (red) (equation 1#
#y=169/41# ------ #color(blue)(equation 2)#
Basically just add #y=169/41# into # y# in the first equation
#-6x-36*169/41=-168#
#-6x-6084/41=-168#
#-6x=-168+6084/41#
#-6x=-804/41#
#x=(804/41)/(6/1)#
#x=cancel804/cancel246#
#x=134/41#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Final result:
#x= 134/41#
#y=169/41#
