How do you solve the system by the substitution method: #2x+3y=6,x=y-7#?

1 Answer
Nov 14, 2016

Answer:

#x = -3 and y = 4#

Explanation:

#color(blue)(x = (y-7))" larr# this means that #x and (y-7)# are identical.
They are therefore interchangeable and one can replace the other.

#" "2color(blue)(x) +3y =6" "larr# replace x with #color(blue)((y-7))#
#color(white)(......)darr#
#2color(blue)((y-7)) +3y = 6" "larr# only y as a variable

#2y-14 +3y = 6#

#5y = 6+14#

#5y = 20#

#y = 4" "larr# if you know #y#, you can work out #x#

#x = y-7#

#x = 4-7 = -3#

Check:
#2x+3y = 2(-3)+3(4)#

# = -6+12 = 6" "larr# which is correct.