How do you solve the following system?: #x +7y = 3 , 12x -9 y = 2#

1 Answer
Jun 25, 2018

Answer:

See a solution process below:

Explanation:

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

#x + 7y = 3#

#x + 7y - color(red)(7y) = 3 - color(red)(7y)#

#x + 0 = 3 - 7y#

#x = 3 - 7y#

Step 2) Substitute #(3 - 7y)# for #x# in the second equation and solve for #y#:

#12x - 9y = 2# becomes:

#12(3 - 7y) - 9y = 2#

#(12 xx 3) - (12 xx 7y) - 9y = 2#

#36 - 84y - 9y = 2#

#36 + (-84 - 9)y = 2#

#36 + (-93)y = 2#

#36 - 93y = 2#

#36 - color(red)(36) - 93y = 2 - color(red)(36)#

#0 - 93y = -34#

#-93y = -34#

#(-93y)/color(red)(-93) = -34/color(red)(-93)#

#(color(red)(cancel(color(black)(-93)))y)/cancel(color(red)(-93)) = 34/93#

#y = 34/93#

Step 3) Substitute #34/93# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = 3 - 7y# becomes:

#x = 3 - (7 xx 34/93)#

#x = (93/93 xx 3) - 238/93#

#x = 279/93 - 238/93#

#x = 41/93#

The Solution Is:

#x = 41/93# and #y = 34/93#

Or

#(41/93, 34/93)#