How do you solve #x + y = 1# and #3x – y = 11# using substitution?

1 Answer
May 10, 2016

Answer:

The solution for the system of equations is:
# color(green)(x = 3 #
# color(green)( y = -2#

Explanation:

#x + y = 1 #
# color(blue)(x = 1 - y# ........equation #(1)#

#3x - y =11#......equation #(2)#

Solving by substitution:

Substituting equation #1# in #2#:

#3x - y =11#

#3 * color(blue)((1 - y)) - y =11#

#3 -3 y - y =11#

#3 -4y =11#

#3 -11 = 4y#

#-8 = 4y #

#y = - 8 / 4 #

# color(green)( y = -2#

Finding #x# from equation #1:#

# color(blue)(x = 1 - y#

# x = 1 - (-2)#

# x = 1 + 2 #

# color(green)(x = 3 #