#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#