How do you solve the system of equations #14x + y = 15# and #14x + 13y = 5#?

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Answer 1 · 2017-04-10T22:27:41

See the entire solution process below: #(95/84, -70/84)#

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

#14x + y = 15#

#-color(red)(14x) + 14x + y = -color(red)(14x) + 15#

#0 + y = -14x + 15#

#y = -14x + 15#

Step 2) Substitute #-14x + 15# for #y# in the second equation and solve for #x#:

#14x + 13y = 5# becomes:

#14x + 13(-14x + 15) = 5#

#14x + (13 xx -14x) + (13 xx 15) = 5#

#14x - 182x + 195 = 5#

#(14 - 182)x + 195 = 5#

#-168x + 195 = 5#

#-168x + 195 - color(red)(195) = 5 - color(red)(195)#

#-168x + 0 = -190#

#-168x = -190#

#(-168x)/color(red)(-168) = (-190)/color(red)(-168)#

#(color(red)(cancel(color(black)(-168)))x)/cancel(color(red)(-168)) = 95/84#

#x = 95/84#

Step 3) Substitute #95/84# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:

#y = -14x + 15# becomes:

#y = (-14 xx 95/84) + 15#

#y = -1330/84 + (84/84 xx 15)#

#y = -1330/84 + 1260/84#

#y = -70/84#

The solution is: #x = 95/84# and #y = -70/84# or #(95/84, -70/84)#