How do you solve the system of equations #8x+4y=13# and #-2x=y+4#?

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Answer 1 · 2017-05-03T13:46:18

See the entire solution process below:

First, sole the second equation for #y#:

#-2x = y + 4#

#-2x - color(red)(4) = y + 4 - color(red)(4)#

#-2x - 4 = y + 0#

#-2x - 4 = y#

#y = -2x - 4#

Step 2) Substitute #-2x - 4# for #y# in the first equation and solve for #x#:

#8x + 4y = 13# becomes:

#8x + 4(-2x - 4) = 13#

#8x + (4 * -2x) - (4 * 4) = 13#

#8x -8x - 16 = 13#

#0 - 16 = 13#

#-16 != 13#

Therefore, there are no solutions to this problem. Or, the solution is the empty or null set: #{O/}#.

This means the two lines defined by these equations are parallel and are not the same line.