Solve the following system of equations by the substitution method.

x - y = 0

x - y - 2 = 0

What 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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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.

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.