Notice that the #y# terms both have the same coefficient.
Subtracting the equations will therefore eliminate the #y# terms.
#" "x" "color(red)(+" "5y)" " =-13" "............................ A#
#-6x" "color(red)(+" "5y)" " =8" ".......................... B#
Subtract #A - B" "# (change the signs of #B#)
#" "x" "+" "5y" " =-13" "color(white)(xxxxxxxxx)A#
#ul(color(blue)(+)6x" "color(blue)(-)" "5y" " =color(blue)(-)8)"
"color(white)(xxxxxxxxx)B#
#" "7xcolor(white)(xxxxxxxxx) =-21" "color(white)(xxxxxxxxxx)C"
"larr div 7#
#" "xcolor(white)(xxxxxxxxx) =-3#
Substitute #-3 " for " x# in #A#
#-3+5y =-13#
#" "5y = -13+3#
#" "5y=-10#
#" "y=-2#
An alternative method is to equate the #y# terms.
Transpose the equations to isolate #5y# in each:
#5y = -13-x" and "5y =8+6x#
We know that #" "5y=5y#
Therefore: #" "6x+8 = -13-x" "larr# now solve for #x#
#6x+x = -13-8#
#" "7x = -21#
#" "x =-3#
Then proceed as described above to get #y=-2#
Check in #B#
#-6x+5y#
#=-6(-3)+5(-2)#
#=18-10#
#=8" "larr# the answer is the same as the RHS