How do solve the following linear system?: # 3x-2y=2 , -4x-14y=28 #?

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Answer 1 · 2016-02-02T14:01:31

Solve by substitution and elimination:

#3x-2y=2#

#-4x-14y=28#

We can eliminate #-14y# from the second equation by #-2y# from the first equation if we multiply it with #-7# to get #14y#

#rarr-7(3x-2y=2)#

Use distributive property:

#rarr-21x+14y=-14#

Add both equations:

#rarr(-4x-14y=28)+(-21x+14y=-14)#

#rarr-25x=14#

#rarrx=-14/25#

Substitute the value of #x# to the first equation:

#rarr3(-14/25)-2y=2#

#rarr-42/25-2y=2#

#rarr-2y=2+42/25#

#rarr-2y=92/25#

#rarry=92/25-:(-2/1)#

#rarry=92/25*(-1/2)#

#rarry=-46/25#

So,
#(x,y)=(-14/25,-46/25)# :)