Solve by Substitution x+3y=2 , 3x+9y=6

$x + 3 y = 2$ , $3 x + 9 y = 6$

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

$x = 2 - 3 y$

$3 x + 9 y = 6$

Replace all occurrences of $x$ with $2 - 3 y$ in each equation.

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Replace all occurrences of $x$ in $3 x + 9 y = 6$ with $2 - 3 y$ .

$3 (2 - 3 y) + 9 y = 6$

$x = 2 - 3 y$

Simplify $3 (2 - 3 y) + 9 y$ .

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Simplify each term.

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Apply the distributive property.

$3 \cdot 2 + 3 (- 3 y) + 9 y = 6$

$x = 2 - 3 y$

Multiply $3$ by $2$ .

$6 + 3 (- 3 y) + 9 y = 6$

$x = 2 - 3 y$

Multiply $- 3$ by $3$ .

$6 - 9 y + 9 y = 6$

$x = 2 - 3 y$

$6 - 9 y + 9 y = 6$

$x = 2 - 3 y$

Combine the opposite terms in $6 - 9 y + 9 y$ .

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Add $- 9 y$ and $9 y$ .

$6 + 0 = 6$

$x = 2 - 3 y$

Add $6$ and $0$ .

$6 = 6$

$x = 2 - 3 y$

$6 = 6$

$x = 2 - 3 y$

$6 = 6$

$x = 2 - 3 y$

$6 = 6$

$x = 2 - 3 y$

Remove any equations from the system that are always true.

$x = 2 - 3 y$

Solve by Substitution x+3y=2 , 3x+9y=6

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