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

Mar 21, 2018

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

Explanation:

Given:

$\left\{\begin{matrix}x - y = 0 \\ x - y - 2 = 0\end{matrix}\right.$

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.

Mar 21, 2018

See a solution process below:

Explanation:

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

$x - y = 0$

$x - y + \textcolor{red}{y} = 0 + \textcolor{red}{y}$

$x - 0 = y$

$x = y$

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

$x - y - 2 = 0$ becomes:

$y - y - 2 = 0$

$0 - 2 = 0$

$- 2 \ne 0$

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

Or, the solution is the empty or null set: $\left\{\emptyset\right\}$

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