How do solve the following linear system?: #8x = -2y - 10, 3x+ 2y - 3 = 0 #?

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Answer 1 · 2016-03-25T18:02:01

The solution for the system of equations is:
#color(green)(x = (-13)/5#

#color(green)( y = 27/(5)#

#8x= -2y-10#
#8x + color(blue)(2y) = -10# ..............equation #(1)#

# 3x+2y-3=0#
# 3x+color(blue)(2y) = 3#.......................equation #(2)#

Solving by elimination.

Subtracting equation #2# from equation #1#

#8x + cancelcolor(blue)(2y) = -10#

# -3x-cancelcolor(blue)(2y) = -3#

#5x = -13#

#color(green)(x = (-13)/5#

Finding #y# from equation #1#

#8x + 2y = -10#

# 2y = -10 - 8x#

# 2y = -10 - 8 * ( -13/5)#

# 2y = -10 + (104/5)#

# 2y = -50/5 + (104/5)#

# 2y = 54/5#

# y = 54/(5 * 2)#

#color(green)( y = 27/(5)#