How do you solve #2x-y=3# and #x+2y=24# using substitution?

2 Answers
Mar 30, 2018

#2x - y = 3#
#x + 2y = 24#

Substitution is a method for solving algebraic equations by finding the value of a variable in terms of other variables and substituting that value into existing equations.
#x = 24 - 2y#

Substituting #24 - 2y# for #x# in the first equation:

#2(24-2y) - y = 3#
#48 -4y - y = 3#
#5y = 48-3#
#5y =45#
#y = 9#

Substituting #9# for #y# in the second equation:
#x + 2*9 = 24#
#x = 24 - 18#
#x = 6#

Mar 30, 2018

Answer:

#x=6# and #y=9#.

Explanation:

#2x-y=3" " " "(1)#
#x+2y=24" " " "(2)#

From eqn #(2)#

#x=24-2y" " " "(3)#

Sub eqn #(3)# into eqn #(1)#

#2(24-2y)-y=3#

#48-4y-y=3#

#45=5y#

#y=9#

Sub #y=9# into eqn #(2)#

#x=24-2(9)#

#x=6#