How do you solve the system #-3(5+x)=y# and #5(x-3)=2y+4#?

1 Answer
Jun 9, 2015

Answer:

The solution for the system of equations is:
# color(blue)( x = -1 , y =-12 #

Explanation:

#-3(5+x)=y#
# -15 -3x = y#
# y +3x = -15# ............equation #(1)#

#5x-15=2y+4#
#5x - 2y = 4 +15#
#5x - color(blue)(2y) = 19#................equation #(2)#

  • Multiplying equation #(1)# by #2#
    # y +3x = -15#
    #color(blue)( 2y)+6x = -30# ...........equation #(3)#
  • Adding equations #2 and 3# to eliminate #color(blue)(2y)#

#5x - cancelcolor(blue)(2y) = 19#
#cancelcolor(blue)( 2y)+6x = -30#
# 11x = -11#
# color(blue)(x = -1#

Substituting #x# in equation #(1)# to find #y#:
#y = -15-3x#
#y = -15-3.(-1)#
#color(blue)(y = -12#