How do you solve the following system?: #-2x -3y =15, -3x +y = -17#

1 Answer
Apr 21, 2016

Answer:

The solution for the system of equations is:

#x = 36/11#

# y = -79/ 11 #

Explanation:

#-2x color(blue)(- 3y) = 15#..................equation #(1)#

#-3x + y = -17#, multiplying by #3#
#-9x + color(blue)(3y) = -51#.............equation #(2)#

Solving by elimination:

Adding both the equations eliminates #color(blue)(3y):#

#-2x cancelcolor(blue)(- 3y) = 15#
#-9x + cancelcolor(blue)(3y) = -51#

#-11x = -36#

#x = (-36)/ (-11)#

#x = 36/11#

Finding #y# from equation #1#:
#-2x - 3y = 15#

#-2x - 15 = 3y#

#-2 * (36/11) - 15 = 3y#

#-72/11 - 15 = 3y#

#-72/11 - 165/11 = 3y#

#-237/ 11 = 3y#

#-237/ (11 * 3) = y#

# y = -79/ 11 #