How do you solve this set of linear systems: # 4 x + y = - 2; 2x - y = - 3#?

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Answer 1 · 2016-11-29T00:52:06

#x = -5/6# and #y = 8/6#

Step 1) Solve the first equation for #y#:

#4x - 4x + y = -2 - 4x#

#y = -2 - 4x#

Step 2) Substitute #-2 - 4x# for #y# in the second equation and solve for #x#:

#2x - (-2 - 4x) = -3#

#2x + 2 + 4x = -3#

#6x + 2 = -3#

#6x + 2 - 2 = -3 - 2#

#6x = -5#

#(6x)/6 = -5/6#

#x = -5/6#

Step 3) Substitute #-5/6# for #x# in the solution to the equation in Step 1) and calculate #y#:

#y = -2 - 4*-5/6#

#y = -2 + 20/6#

#y = 6/6*-2 + 20/6#

#y = -12/6 + 20/6#

#y = 8/6#