Given:

[1]#color(white)("XXX")-5x-5y=-6#

[2]#color(white)("XXX")3x-y=-1#

Rearrange [2] to isolate the #y# term on the left side:

[3]#color(white)("XXX")-y=-1-3x#

(the next two steps are not necessary, but I find it easier to work with positives)

Multiply both [1] and [3] by #(-1)# to reverse the signs

[4]#color(white)("XXX")5x+5y=6#

[5]#color(white)("XXX")y=1+3x#

Substitute #(1+3x)# from [5] for #y# in [4]

[6]#color(white)("XXX")5x+5(1+3x)=6#

Simplify [6]

[7]#color(white)("XXX")20x+5=6#

Subtract #5# from both sides of [7]

[8]#color(white)("XXX")20x=1#

Divide both sides of [8] by #20#

[9]#color(white)("XXX")color(green)(x=1/20)#

Substitute #1/20# from [9] for #x# in [2]

[10]#color(white)("XXX")3xx1/20-y=-1#

Subtract #(3/20)# from both sides of [10]

[11]#color(white)("XXX")-y=-23/20#

Multiply both sides of [11] by #(-1)#

[12]#color(white)("XXX")color(green)(y=23/20)#