How do you solve #x - y = 0# and #x - y - 2 = 0 # using substitution?

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Answer 1 · 2018-03-21T11:28:13

This system of equations is inconsistent, so has an empty solution set.

Given:

#{ (x-y = 0), (x-y-2 = 0) :}#

Using the first equation, we get a value #0# for #x-y#, which we can then substitute into the second equation to get:

#0 - 2 = 0#

which is false.

So this system is inconsistent and there are no values of #x, y# which satisfy it.

Answer 2 · 2018-03-21T11:28:23

See a solution process below:

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

#x - y = 0#

#x - y + color(red)(y) = 0 + color(red)(y)#

#x - 0 = y#

#x = y#

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

#x - y - 2 = 0# becomes:

#y - y - 2 = 0#

#0 - 2 = 0#

#-2 != 0#

Because #-2# is definitely not equal to #0# there are now solutions for this problem.

Or, the solution is the empty or null set: #{O/}#

This indicates the two lines represented by the equations in the problem are parallel lines and not the same lines.