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Solve the following system of equations by the substitution method.x - y = 0x - y - 2 = 0What is the solution set?

Solve the following system of equations by the substitution method.

x - y = 0

x - y - 2 = 0

What is the solution set?

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Matt L. | MIT/Harvard Grad for Academic Tutoring & Test PrepMIT/Harvard Grad for Academic Tutoring &...
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John R. | John R: Math, Science, and History TeacherJohn R: Math, Science, and History Teach...
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The first step in solving a system of equations by substitution is solving one of the equations for one of the variables

x - y = 0                Equation 1

x - y + y = 0 +y      Add y to each side

x = y                     Simplify

After solving an equation for one of the variables, substitute that value into the other equation.  In this problem, I can substitute y for x.

x - y - 2 = 0                  Equation 2

y - y - 2 = 0                  Substitute the value of x from equation 1

0 - 2 = 0                      Inverse Property of addition

-2 = 0                          Identity Property of addition

Since -2 can not equal 0, there is no solution.  The lines are parallel.  It is an inconsistent system.

 

Kevin S. |
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Since x - y = 0, we can solve for x, to get
x = y.

We now substitute that into the second equation to get
y - y - 2 = 0 or
-2 = 0

which is a false statement and is never true.

Therefore, there is no solution set for this system.