Solve the System of Equations x-y=4 y=x-4

$x - y = 4$ $y = x - 4$

Replace all occurrences of $y$ with $x - 4$ in each equation.

Replace all occurrences of $y$ in $x - y = 4$ with $x - 4$ .

$x - (x - 4) = 4$

$y = x - 4$

Simplify the left side.

Simplify $x - (x - 4)$ .

Simplify each term.

Apply the distributive property.

$x - x + 4 = 4$

$y = x - 4$

Multiply $- 1$ by $- 4$ .

$x - x + 4 = 4$

$y = x - 4$

$x - x + 4 = 4$

$y = x - 4$

Simplify by adding terms.

Subtract $x$ from $x$ .

$0 + 4 = 4$

$y = x - 4$

Add $0$ and $4$ .

$4 = 4$

$y = x - 4$

$4 = 4$

$y = x - 4$

$4 = 4$

$y = x - 4$

$4 = 4$

$y = x - 4$

$4 = 4$

$y = x - 4$

Remove any equations from the system that are always true.

$y = x - 4$

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