#y = 2x-13 and y = -2x+23#
This is the best scenario you can get if you want to use the elimination method.
Notice that the two #x=#terms are additive inverses.
#y = color(blue)(2x)-13 and y = color(blue)(-2x)+23#
If you add the two equations together, the #x-#terms will add up to 0 and thereby be eliminated.
#color(white)(...........)y =" " 2x-13 ............................A#
#color(white)(...........)y = -2x+23 ............................B#
#A+B:" :2y = color(blue)(0x) +10#
#color(white)(..............)y = 5#
Substitute to find #x#
#color(white)(.............)5 = 2x-13 ............................A#
#color(white)(.....)5+13 =2x #
#color(white)(.............)18 =2x #
#color(white)(...............)9 =x #
Check in B
#color(white)(...........)y = -2(9)+23 ............................B#
#color(white)(...........)y = -18+23 #
#color(white)(...........)y = 5#