Kakšen je odgovor? Uporabite izločitev ali zamenjavo za rešitev -5x + 14y = 17 "" in "" 9x-6y = 27

Odgovor:

# x = 5 in y = 3 #

Pojasnilo:

Naj bodo enačbe:

# -5x + 14y-17 = 0 "" #(je enačba 1)

# "" 9x-6y-27 = 0 "" # (je enačba 2)

(enačba 1 pomeni) => # 14y = 5x + 17 #

=> # "" y = (5x + 17) / 14 # (je enačba 3)

(Namesto v enačbo 2)

# 9x-6 {(5x + 17) / 14} -27 = 0 "" larr xx 14 #

=> # 126x-30x-102-378 = 0 #

=> # 96x-480 = 0 #

=> # 96x = 480 #

=> # x = 480/96 #

=> # x = 5 #

Sedaj nadomestite v enačbo 3

=> # y = {5 (5) +17} / 14 "" #(ob x = 5)

=> # y = {(25) +17} / 14 #

=> # y = 42/14 #

# y = 3 #

Odgovor:

# y = 3, x = 5 #

Pojasnilo:

#:.- 5x + 14y = 17 --------- (1) #

#:. 9x-6y = 27 ----------- (2) #

#:. (1) xx9 #

#:.- 45x + 126y = 153 ------ (3) #

#:. (2) xx5 #

#:. 45x-30y = 135 ------- (4) #

#:.(3)+(4)#

#:. 96y = 288 #

#:. y = 3 #

nadomestek # y = 3 # v# (2)#

#:. 9x-6 (3) = 27 #

#:. 9x-18 = 27 #

#:. 9x = 27 + 18 #

#:. 9x = 45 #

#:. x = 5 #

~~~~~~~~~

preverite: -

Namestnik # y = 3 #in # x = 5 # v #(2)#

#:.9(5)-6(3)=27#

#:.45-18=27#

#:.27=27#