Find the Points of Intersection x-y=2 , 3x-3y=6

$x - y = 2$ , $3 x - 3 y = 6$

Step 1

Add $y$ to both sides of the equation.

$x = 2 + y$

$3 x - 3 y = 6$

Step 2

Replace all occurrences of $x$ with $2 + y$ in each equation.

Replace all occurrences of $x$ in $3 x - 3 y = 6$ with $2 + y$ .

$3 (2 + y) - 3 y = 6$

$x = 2 + y$

Simplify the left side.

Simplify $3 (2 + y) - 3 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 2 + 3 y - 3 y = 6$

$x = 2 + y$

Multiply $3$ by $2$ .

$6 + 3 y - 3 y = 6$

$x = 2 + y$

$6 + 3 y - 3 y = 6$

$x = 2 + y$

Combine the opposite terms in $6 + 3 y - 3 y$ .

Subtract $3 y$ from $3 y$ .

$6 + 0 = 6$

$x = 2 + y$

Add $6$ and $0$ .

$6 = 6$

$x = 2 + y$

$6 = 6$

$x = 2 + y$

$6 = 6$

$x = 2 + y$

$6 = 6$

$x = 2 + y$

$6 = 6$

$x = 2 + y$

Step 3

Remove any equations from the system that are always true.

$x = 2 + y$

Step 4