These equations are ideal for creating additive inverses to eliminate the #x#-terms. Additive inverses add to #0#
#color(white)(xxxxxx.xx)color(blue)(2x)+3y=+ 7color(white)(xxxx.xxxxxxx)A#
#color(white)(xxxxxx..)color(blue)(-3x)-5y= -13color(white)(xxxxxxxxxxx)B#
#Axx3: color(white)(xxxxx)color(blue)(6x)+9y=+ 21color(white)(xxxx...xxxxx)C#
#Bxx2:color(white)(x.x.)color(blue)(-6x)-10y= -26color(white)(xxxxxxxxxx)D#
#C+D:color(white)(xxxxxxx)-y=-5" "larr# the #x# term is #0#
#color(white)(xxxxxxxxxxxxxx)y=5#
Substitute #y=5# into A
#color(white)(xxxx.xx)2x+3(5)= 7color(white)(xxxxxxx)A#
#color(white)(xxxxxxxx..xx)2x = -8#
#color(white)(xxxxxx.xx..xx)x=-4#
Substitute for #x and y# in B to check:
#-3(-4)-5(5)#
#12-25#
#=-13#
The equation checks out.
