How do solve the following linear system?: # 3x-y=7 , 11x + 3y + 7 = 0 #?

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Answer 1 · 2016-04-11T05:54:37

The solution for the system of equations is:
#color(green)(x = 7 / 10#

#color(green)(y = (- 49) / 10#

#3x - y = 7# , multiplying by #3#
#9x - color(blue)(3y )= 21#.....................equation #(1)#

#11x + color(blue)( 3y) = - 7#................equation #(2)#

Solving by elimination.

Adding equations #1# and #2# eliminates #color(blue)(3y#

#9x - cancelcolor(blue)(3y )= 21#

#11x + cancelcolor(blue)( 3y) = - 7#

#20x = 14#

#x = 14 / 20#

#color(green)(x = 7 / 10#

Finding #y# from equation #1#

#3x - y = 7#

#3x - 7 = y#

#3 * color(green)(7/10) - 7 = y#

#21/10 - 7 = y#

#(21 - 70) / 10 = y#

# (- 49) / 10 = y#

#color(green)(y = (- 49) / 10#