How do you solve the system of equations #5x+2y=75, -x-2y=-31#?

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Answer 1 · 2016-12-10T14:12:49

#x = 11# and #y = 10#

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

#-x + x - 2y + 31 = -31 + 31 + x#

#-2y + 31 = x#

#x = -2y + 31#

Step 2) Substitute #-2y + 31# into the first equation for #x# and then solve for #y#:

#5(-2y + 31) + 2y = 75#

#-10y + 155 + 2y = 75#

#8y + 155 = 75#

#8y + 155 - 155 = 75 - 155#

#8y = -80#

#(8y)/8 = 80/8#

#y = 10#

Step 3) Substitute #10# for #y# into the solution for the second equation and the end of Step 1).

#x = -2*10 + 31#

#x = -20 + 31#

#x = 11#