How do you solve the system using elimination #2x-y=9 # and #x-2y=11#?

1 Answer
Jun 10, 2015

Answer:

The solution for the system of equations is
#color(blue)( x =7/3 and y =-13/3#

Explanation:

#2x-y=9 # , multiplying this equation by #2#
# 4x color(blue)(-2y) =18#.......equation #(1)#
#xcolor(blue)(-2y)=11# ........equation #(2)#

Subtracting equation #(1)# from #(2)# to eliminate #color(blue)(2y#

#xcolor(blue)cancel(-2y)=11#
# -4x color(blue)cancel(+2y) =-18#

# -3x = -7#
# color(blue)(x = 7/3#

Substituting #x# in the first equation to find #y#

# y = 2x -9#

# y = 2.(7/3) - 9#

# y = 14/3 - 9#
#color(blue)( y = -13/3#