How do solve the following linear system?: # -10x+7y=-2 , x-y=11 #?

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Answer 1 · 2017-02-07T13:14:13

See the entire solution process below:

Step 1) Solve for #x# in the second equation:

#x - y + color(red)(y) = 11 + color(red)(y)#

#x - 0 = 11 + y#

#x = 11 + y#

Step 2) Substitute #11 + y# for #x# in the first equation and solve for #y#:

#-10x + 7y = -2# becomes:

#-10(11 + y) + 7y = -2#

#-110 - 10y + 7y = -2#

#-110 - 3y = -2#

#-110 + color(red)(110) - 3y = -2 + color(red)(110)#

#0 - 3y = 108#

#-3y = 108#

#(-3y)/color(red)(-3) = 108/color(red)(-3)#

#(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = -36#

#y = -36#

Step 3) Substitute #-36# for #y# in the solution to the second equation at the end of Step 1 and solve for #x#:

#x = 11 + y# becomes:

#x = 11 - 36#

#x = -25#

The solution is: #x = -25# and #y = -36#