How do you solve the system of equations #8x - 15y = - 204# and #8x - 7y = - 44#?

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Answer 1 · 2017-07-19T14:23:03

See a solution process below:

First, we can subtract the two equations from each other:

#" "8x - 7y = -44#
#"-"(8x - 15y = -204)#

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#" "8x - 7y = -44#
# -8x + 15y = 204#

#0x + 8y = 160#

We can next solve this for #y#:

#8y = 160#

#(8y)/color(red)(8) = 160/color(red)(8)#

#(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = 20#

#y = 20#

Now, we can substitute #20# for #y# in either equation and solve for #x#:

#8x - 7y = -44# becomes:

#8x - (7 * 20) = -44#

#8x - 140 = -44#

#8x - 140 + color(red)(140) = -44 + color(red)(140)#

#8x - 0 = 96#

#8x = 96#

#(8x)/color(red)(8) = 96/color(red)(8)#

#(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = 12#

#x = 12#

The Solution Is: #x = 12# and #y = 20# or #(12, 20)#