How do you solve the following system?: #-x -3y =5, -3x +4y = -7#

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Answer 1 · 2016-03-31T17:21:52

The solution for the system of equations is:
#color(green)( x = 1/13#

#color(green)(y = -22/13#

#-x - 3y = 5# , multiplying by #3#
#color(blue)(-3x) - 9y = 15#......equation #(1)#

#color(blue)(-3x) + 4y =-7#......equation #(2)#

Solving by elimination.

Subtracting equation #(2)# from #(1)#

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

#cancelcolor(blue)(+3x) - 4y =+7#

#-13y = 22#

#color(green)(y = -22/13#

Finding #x# from equation #1#

#-x - 3y = 5#

# x = - 3y - 5#

# x = - 3 * (color(green)( -22/13)) - 5#

# x = 66/13 - 5#

# x = 66/13 - 65/13#

#color(green)( x = 1/13#