How do you solve this system of equations using the substitution method: #10x + 2y = 15 and - 5x = y + 10#?

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Answer 1 · 2017-10-10T21:46:52

See a solution process below:

Step 1: Solve the second equation for #y#:

#-5x - color(red)(10) = y + 10 - color(red)(10)#

#-5x - 10 = y + 0#

#-5x - 10 = y#

#y = -5x - 10#

Step 2: Substitute #(-5x - 10)# for #y# in the first equation and solve for #x#:

#10x + 2y = 15# becomes:

#10x + 2(-5x - 10) = 15#

#10x - 10x - 20 = 15#

#-20 != 15#

Because #-20# is obviously no equal to #15# there are no solutions to this problem. Or, the solution is the empty or null set: #{O/}#

This indicates these two lines are parallel but are not the same line.