How do you solve the following system?: #x-7y=9 , 7y=3x+1 #

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Answer 1 · 2017-05-20T13:14:43

See a solution process below:

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

#x - 7y = 9#

#x - 7y + color(red)(7y) = 9 + color(red)(7y)#

#x - 0 = 9 + 7y#

#x = 9 + 7y#

Step 2) Substitute #9 + 7y# for #x# in the second equation and solve for #y#:

#7y = 3x + 1# becomes:

#7y = 3(9 + 7y) + 1#

#7y = (3 * 9) + (3 * 7y) + 1#

#7y = 27 + 21y + 1#

#7y = 28 + 21y#

#7y - color(red)(21y) = 28 + 21y - color(red)(21y)#

#(7 - color(red)(21))y = 28 + 0#

#-14y = 28#

#(-14y)/color(red)(-14) = 28/color(red)(-14)#

#(color(red)(cancel(color(black)(-14)))y)/cancel(color(red)(-14)) = -2#

#y = -2#

Step 3) Substitute #-2# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = 9 + 7y# becomes:

#x = 9 + (7 * -2)#

#x = 9 + (-14)#

#x = 9 - 14#

#x = -5#

The solution is: #x = -5# and #y = -2# or #(-5, -2)#