How do you solve the system using elimination #y = -x + 5# and #2x - 3y = -6#?

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Answer 1 · 2015-06-03T08:01:05

#y = -x + 5#
#y + x = 5#.............equation #(1)#

#2x color(red)(- 3y) = -6#...... equation #(2)#

multiplying equation #(1)# by #3#
#(y + x = 5) xx 3#

# 3x color(red)(+3y) = 15#........ equation #(3)#

Adding equations #(2)# and #(3)# to eliminate #color(red)(3y#:

#2x cancel(-3y) = -6#
# 3x +cancel(3y) = 15#

# 5x = 9 , color(blue)(x = 9/5#
Substituting #x# in equation #(1)# to find #y#
#y = -x + 5#
#y = -9/5 + 5 = (-9+25)/5 , color(blue)(y = 16/5#

The solution for the system of equations is #color(blue)( x= 9/5 and y = 16/5#