How do solve the following linear system?: # 3x - y = -6, y = 5x - 7#?

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Answer 1 · 2017-08-27T17:56:20

See a solution process below: #(13/2, 51/2)#

Step 1) Because the second equation is already solved for #y# we can substitute #(5x - 7)# for #y# in the first equation and solve for #x#:

#3x - y = -6# becomes:

#3x - (5x - 7) = -6#

#3x - 5x + 7 = -6#

#(3 - 5)x + 7 = -6#

#-2x + 7 = -6#

#-2x + 7 - color(red)(7) = -6 - color(red)(7)#

#-2x + 0 = -13#

#-2x = -13#

#(-2x)/color(red)(-2) = (-13)/color(red)(-2)#

#(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = 13/2#

#x = 13/2#

Step 2) Substitute #13/2# for #x# in the second equation and calculate #y#:

#y = 5x - 7# becomes:

#y = (5 * 13/2) - 7#

#y = 65/2 - (2/2 xx 7)#

#y = 65/2 - 14/2#

#y = 51/2#

The Solution Is: #x = 13/2# and #y = 51/2# or #(13/2, 51/2)#