How do you solve the following system: #x + 8y = 15 , 5x - 7y = 12 #?

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Answer 1 · 2018-05-23T12:16:28

See a solution process below:

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

#x + 8y = 15#

#x + 8y - color(red)(8y) = 15 - color(red)(8y)#

#x + 0 = 15 - 8y#

#x = 15 - 8y#

Step 2) Substitute #(15 - 8y)# for #x# in the second equation and solve for #y#:

#5x - 7y = 12# becomes:

#5(15 - 8y) - 7y = 12#

#(5 xx 15) - (5 xx 8y) - 7y = 12#

#75 - 40y - 7y = 12#

#75 + (-40 - 7)y = 12#

#75 + (-47)y = 12#

#75 - 47y = 12#

#75 - color(red)(75) - 47y = 12 - color(red)(75)#

#0 - 47y = -63#

#-47y = -63#

#(-47y)/color(red)(-47) = -63/color(red)(-47)#

#y = 63/47#

Step 3) Substitute #63/47# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = 15 - 8y# becomes:

#x = 15 - (8 xx 63/47)#

#x = 15 - 504/47#

#x = (47/47 xx 15) - 504/47#

#x = 705/47 - 504/47#

#x = 201/47#

The Solution Is:

#x = 201/47# and #y = 63/47#

Or

#(201/47, 63/47)#