How do you solve -4x+y=-11 and 2x-3y=5?

1 Answer
Alan P.
Nov 30, 2015

#(x,y) = (14/5,1/5)#

Explanation:

Given:
[1]#color(white)("XXX")-4x+y=-11#
[2]#color(white)("XXX")2x-3y=5#

Multiply [2] by #2# giving #x# a coefficient of the same magnitude as in [1]
[3]#color(white)("XXX")4x-6y =10#

Add [1] and [3], eliminating the #x# term
[4]#color(white)("XXX")-5y = -1#

Divide both sides of [4] by #(-5)#
[6]#color(white)("XXX")y=1/5#

Multiply [1] by #3# giving #y# a coefficient of the same magnitude as in [2]
[7]#color(white)("XXX")-12x+3y=-33#

Add [2] and [7], eliminating the #y# term
[8]#color(white)("XXX")-10x = -28#

Divide both sides of [8] by #(-10)#
[9]#color(white)("XXX")x=14/5#

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