Solve the System of Equations x-2y=6 and 3x-6y=18

$x - 2 y = 6$ and $3 x - 6 y = 18$

Add $2 y$ to both sides of the equation.

$x = 6 + 2 y$

$3 x - 6 y = 18$

Replace all occurrences of $x$ with $6 + 2 y$ in each equation.

Replace all occurrences of $x$ in $3 x - 6 y = 18$ with $6 + 2 y$ .

$3 (6 + 2 y) - 6 y = 18$

$x = 6 + 2 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$3 \cdot 6 + 3 (2 y) - 6 y = 18$

$x = 6 + 2 y$

Multiply $3$ by $6$ .

$18 + 3 (2 y) - 6 y = 18$

$x = 6 + 2 y$

Multiply $2$ by $3$ .

$18 + 6 y - 6 y = 18$

$x = 6 + 2 y$

$18 + 6 y - 6 y = 18$

$x = 6 + 2 y$

Combine the opposite terms in $18 + 6 y - 6 y$ .

Subtract $6 y$ from $6 y$ .

$18 + 0 = 18$

$x = 6 + 2 y$

Add $18$ and $0$ .

$18 = 18$

$x = 6 + 2 y$

$18 = 18$

$x = 6 + 2 y$

$18 = 18$

$x = 6 + 2 y$

$18 = 18$

$x = 6 + 2 y$

$18 = 18$

$x = 6 + 2 y$

Remove any equations from the system that are always true.

$x = 6 + 2 y$

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