"Find an ordered pair" means find #(x,y)#, which in other words means, solve the system of equations.
The ideal situation is to have one of the variables in the two equations as additive inverses.
Notice that the #y#-terms already have opposite signs.
#-7x color(blue)(+ 6y) = 11 and 8x color(blue)(- 3y) = -1#
Multipying the second equation by #2# will give #-6y#
#color(white)(..............)-7x + 6y =" " 11#......................A
#color(white)(...................)8x -3y = -1#.......................B
#B xx2:color(white)(.....)16x - 6y = -2#......................C
#color(white)(..............)-7x + 6y =" " 11#......................A
#A+C:color(white)(.....)9x =9#
#A+C:color(white)(......)x = 1#
Substitute #x=1 into A (or any other equation.
#-7(1) + 6y = 11#
#6y= 11+7#
#6y = 18#
#y =3#
Check in B:
Is #8(1) -3(3) = -1#?
#" "8 -9#
#= -1#
.
