How do you solve the following system?: #x -9y =-2 , -2x +5y = -9#

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Answer 1 · 2017-04-28T14:27:01

See the entire solution process below:

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

#x - 9y = -2#

#x - 9y + color(red)(9y) = -2 + color(red)(9y)#

#x - 0 = -2 + 9y#

#x = -2 + 9y#

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

#-2x + 5y = -9# becomes:

#-2(-2 + 9y) + 5y = -9#

#(-2 * -2) + (-2 * 9y) + 5y = -9#

#4 - 18y + 5y = -9#

#4 + (-18 + 5)y = -9#

#4 + (-13)y = -9#

#4 - 13y = -9#

#-color(red)(4) + 4 - 13y = -color(red)(4) - 9#

#0 - 13y = -13#

#-13y = -13#

#(-13y)/color(red)(-13) = (-13)/color(red)(-13)#

#(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = 1#

#y = 1#

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

#x = -2 + 9y# becomes:

#x = -2 + (9 * 1)#

#x = -2 + 9#

#x = 7#

The solution is: #x = 7# and #y = 1# or #(7, 1)#