#color(white)(.....)-3x+2y =-15" "A#
#color(white)(.....)+2x-4y =+26" "B#
Try to create additive inverses with the variables.
#A xx 2: rarr color(white)(...)-6xcolor(blue)(+4y) =-30" "C#
#color(white)(........... ............)2xcolor(blue)(-4y) =+26" "B#
#C+B:color(white)(........)-4x " "= -4#
#color(white)(....................................)x =1#
Substitute #x=1# into B
#color(white)(.....)+2x-4y =+26" "B#
#color(white)(.....)+2(1)-4y =+26#
#color(white)(..........)+2-4y =+26#
#color(white)(.................)-4y =+26-2#
#color(white)(.................)-4y =+24#
#color(white)(.........................)y =-6#
Check in equation A:
#-3(1) +2(-6) = -15#
#-3-12 = -15#
#color(white)(......)-15 = -15#