How do you solve the system of equations #8x - y = 18# and #- 3x - y = 7#?

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Answer 1 · 2016-12-14T13:46:34

#x = 1# and #y = -10#

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

#8x - y + y - 18 = 18 - 18 + y#

#8x - 0 - 18 = 0 + y#

#8x - 18 = y# or #y = 8x - 18#

Step 2) Substitute #8x - 18# for #y# in the second equation and solve for #x#:

#-3x - (8x - 18) = 7#

#-3x - 8x + 18 = 7#

#-11x + 18 - 18 = 7 - 18#

#-11x + 0 = -11#

#-11x = -11#

#(-11x)/(-11) = (-11)/(-11)#

#x = 1#

Step 3) Substitute #1# for #x3 in the solution to the first equation in Step 1) and calculate #y#:

#y = (8 xx 1) - 18#

#y = 8 - 18#

#y = -10#