How do you solve the system of equations #5x + y = - 14# and #- 7x - 4y = 17#?

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Answer 1 · 2016-12-09T14:31:36

#x = -3# and #y = 1#

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

#5x - 5x + y = -14 - 5x#

#0 + y = -14 - 5x#

#y = -14 - 5x#

Step 2) Substitute #-14 - 5x# for #y# in the second equation and solve for #x#:

#-7x - 4(-14 - 5x) = 17#

#-7x + 56 + 20x = 17#

#13x + 56 = 17#

#13x + 56 - 56 = 17 - 56#

#13x + 0 = -39#

#13x = -43#

#(13x)/13 = -39/13#

#x = -3#

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

#y = -14 - (5*-3)#

#y = -14 + 15#

#y = 1#