How do you solve the system of linear equations #2x+3y= 7# and #-3x-5y= -13#?

1 Answer
Aug 15, 2017

Answer:

#x =-4 and y =5#

Explanation:

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.