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

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

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

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

$3 (2 x + 6) = 6 x + 18$

$y = 2 x + 6$

Simplify the left side.

Simplify $3 (2 x + 6)$ .

Apply the distributive property.

$3 (2 x) + 3 \cdot 6 = 6 x + 18$

$y = 2 x + 6$

Multiply.

Multiply $2$ by $3$ .

$6 x + 3 \cdot 6 = 6 x + 18$

$y = 2 x + 6$

Multiply $3$ by $6$ .

$6 x + 18 = 6 x + 18$

$y = 2 x + 6$

$6 x + 18 = 6 x + 18$

$y = 2 x + 6$

$6 x + 18 = 6 x + 18$

$y = 2 x + 6$

$6 x + 18 = 6 x + 18$

$y = 2 x + 6$

$6 x + 18 = 6 x + 18$

$y = 2 x + 6$

Remove any equations from the system that are always true.

$y = 2 x + 6$

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