Solve the System of Equations x-y=9 and -9x-3y=39

$x - y = 9$ and $- 9 x - 3 y = 39$

Step 1

Add $y$ to both sides of the equation.

$x = 9 + y$

$- 9 x - 3 y = 39$

Step 2

Replace all occurrences of $x$ with $9 + y$ in each equation.

Replace all occurrences of $x$ in $- 9 x - 3 y = 39$ with $9 + y$ .

$- 9 (9 + y) - 3 y = 39$

$x = 9 + y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$- 9 \cdot 9 - 9 y - 3 y = 39$

$x = 9 + y$

Multiply $- 9$ by $9$ .

$- 81 - 9 y - 3 y = 39$

$x = 9 + y$

$- 81 - 9 y - 3 y = 39$

$x = 9 + y$

Subtract $3 y$ from $- 9 y$ .

$- 81 - 12 y = 39$

$x = 9 + y$

$- 81 - 12 y = 39$

$x = 9 + y$

$- 81 - 12 y = 39$

$x = 9 + y$

$- 81 - 12 y = 39$

$x = 9 + y$

Step 3

Solve for $y$ in $- 81 - 12 y = 39$ .

Move all terms not containing $y$ to the right side of the equation.

Add $81$ to both sides of the equation.

$- 12 y = 39 + 81$

$x = 9 + y$

Add $39$ and $81$ .

$- 12 y = 120$

$x = 9 + y$

$- 12 y = 120$

$x = 9 + y$

Divide each term in $- 12 y = 120$ by $- 12$ and simplify.

Divide each term in $- 12 y = 120$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{120}{- 12}$

$x = 9 + y$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{120}{- 12}$

$x = 9 + y$

Divide $y$ by $1$ .

$y = \frac{120}{- 12}$

$x = 9 + y$

$y = \frac{120}{- 12}$

$x = 9 + y$

$y = \frac{120}{- 12}$

$x = 9 + y$

Simplify the right side.

Divide $120$ by $- 12$ .

$y = - 10$

$x = 9 + y$

$y = - 10$

$x = 9 + y$

$y = - 10$

$x = 9 + y$

$y = - 10$

$x = 9 + y$

Step 4

Replace all occurrences of $y$ with $- 10$ in each equation.

Replace all occurrences of $y$ in $x = 9 + y$ with $- 10$ .

$x = 9 - 10$

$y = - 10$

Simplify $x = 9 - 10$ .

Simplify the left side.

Remove parentheses.

$x = 9 - 10$

$y = - 10$

$x = 9 - 10$

$y = - 10$

Simplify the right side.

Subtract $10$ from $9$ .

$x = - 1$

$y = - 10$

$x = - 1$

$y = - 10$

$x = - 1$

$y = - 10$

$x = - 1$

$y = - 10$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 1, - 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 10)$

Equation Form:

$x = - 1, y = - 10$

Step 7

Solve the System of Equations x-y=9 and -9x-3y=39

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