How do you solve #-5x + 14y = 16 ; -3x + 9y = 12#?

1 Answer
Jan 2, 2017

Answer:

#(x,y)=(8,4)#

Explanation:

Given
[1]#color(white)("XXX")-5x+14y=16#
[2]#color(white)("XXX")-3x+9y=12#

Multiply each equation by a constant to make coefficients of #x# inverse of each other.
[2]=[1]#xx(-3)##color(white)("XXX")15x-42y=-48#
[3]=[2]#xx5##color(white)("XXXxx")-15x+49y=color(white)("XX")60#

Add [2] and [3] to get rid of #x# term
[4]#color(white)("XXXXXXXXXXXXXX")7y=28#

Divide both sides of [4] by #7#
[5]#color(white)("XXXXXXXXXXXXXXX")y=4#

Substitute #4# in place of #y# in [2] (we could have used [1])
[6]#color(white)("XXX")-3x+9 * 4 = 12#

Simplifying
[7]#color(white)("XXX")-3x+36=12#

[8]#color(white)("XXX")-3x=-24#

[9]#color(white)("XXX")x=8#