Find the Points of Intersection x+3y=3 2x+6y=6

$x + 3 y = 3$ $2 x + 6 y = 6$

Subtract $3 y$ from both sides of the equation.

$x = 3 - 3 y$

$2 x + 6 y = 6$

Replace all occurrences of $x$ with $3 - 3 y$ in each equation.

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

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

$x = 3 - 3 y$

Simplify the left side.

Simplify $2 (3 - 3 y) + 6 y$ .

Simplify each term.

Apply the distributive property.

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

$x = 3 - 3 y$

Multiply $2$ by $3$ .

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

$x = 3 - 3 y$

Multiply $- 3$ by $2$ .

$6 - 6 y + 6 y = 6$

$x = 3 - 3 y$

$6 - 6 y + 6 y = 6$

$x = 3 - 3 y$

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

Add $- 6 y$ and $6 y$ .

$6 + 0 = 6$

$x = 3 - 3 y$

Add $6$ and $0$ .

$6 = 6$

$x = 3 - 3 y$

$6 = 6$

$x = 3 - 3 y$

$6 = 6$

$x = 3 - 3 y$

$6 = 6$

$x = 3 - 3 y$

$6 = 6$

$x = 3 - 3 y$

Remove any equations from the system that are always true.

$x = 3 - 3 y$

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