Solve by Substitution x-3y=7 and 3x-9y=21

$x - 3 y = 7$ and $3 x - 9 y = 21$

Add $3 y$ to both sides of the equation.

$x = 7 + 3 y$

$3 x - 9 y = 21$

Replace all occurrences of $x$ with $7 + 3 y$ in each equation.

Replace all occurrences of $x$ in $3 x - 9 y = 21$ with $7 + 3 y$ .

$3 (7 + 3 y) - 9 y = 21$

$x = 7 + 3 y$

Simplify the left side.

Simplify $3 (7 + 3 y) - 9 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 7 + 3 (3 y) - 9 y = 21$

$x = 7 + 3 y$

Multiply $3$ by $7$ .

$21 + 3 (3 y) - 9 y = 21$

$x = 7 + 3 y$

Multiply $3$ by $3$ .

$21 + 9 y - 9 y = 21$

$x = 7 + 3 y$

$21 + 9 y - 9 y = 21$

$x = 7 + 3 y$

Combine the opposite terms in $21 + 9 y - 9 y$ .

Subtract $9 y$ from $9 y$ .

$21 + 0 = 21$

$x = 7 + 3 y$

Add $21$ and $0$ .

$21 = 21$

$x = 7 + 3 y$

$21 = 21$

$x = 7 + 3 y$

$21 = 21$

$x = 7 + 3 y$

$21 = 21$

$x = 7 + 3 y$

$21 = 21$

$x = 7 + 3 y$

Remove any equations from the system that are always true.

$x = 7 + 3 y$

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