Solve by Substitution -3x-3y=3 y=-5x-17

$- 3 x - 3 y = 3$ $y = - 5 x - 17$

Step 1

Replace all occurrences of $y$ with $- 5 x - 17$ in each equation.

Replace all occurrences of $y$ in $- 3 x - 3 y = 3$ with $- 5 x - 17$ .

$- 3 x - 3 (- 5 x - 17) = 3$

$y = - 5 x - 17$

Simplify the left side.

Simplify $- 3 x - 3 (- 5 x - 17)$ .

Simplify each term.

Apply the distributive property.

$- 3 x - 3 (- 5 x) - 3 \cdot - 17 = 3$

$y = - 5 x - 17$

Multiply $- 5$ by $- 3$ .

$- 3 x + 15 x - 3 \cdot - 17 = 3$

$y = - 5 x - 17$

Multiply $- 3$ by $- 17$ .

$- 3 x + 15 x + 51 = 3$

$y = - 5 x - 17$

$- 3 x + 15 x + 51 = 3$

$y = - 5 x - 17$

Add $- 3 x$ and $15 x$ .

$12 x + 51 = 3$

$y = - 5 x - 17$

$12 x + 51 = 3$

$y = - 5 x - 17$

$12 x + 51 = 3$

$y = - 5 x - 17$

$12 x + 51 = 3$

$y = - 5 x - 17$

Step 2

Solve for $x$ in $12 x + 51 = 3$ .

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

Subtract $51$ from both sides of the equation.

$12 x = 3 - 51$

$y = - 5 x - 17$

Subtract $51$ from $3$ .

$12 x = - 48$

$y = - 5 x - 17$

$12 x = - 48$

$y = - 5 x - 17$

Divide each term in $12 x = - 48$ by $12$ and simplify.

Divide each term in $12 x = - 48$ by $12$ .

$\frac{12 x}{12} = \frac{- 48}{12}$

$y = - 5 x - 17$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{- 48}{12}$

$y = - 5 x - 17$

Divide $x$ by $1$ .

$x = \frac{- 48}{12}$

$y = - 5 x - 17$

$x = \frac{- 48}{12}$

$y = - 5 x - 17$

$x = \frac{- 48}{12}$

$y = - 5 x - 17$

Simplify the right side.

Divide $- 48$ by $12$ .

$x = - 4$

$y = - 5 x - 17$

$x = - 4$

$y = - 5 x - 17$

$x = - 4$

$y = - 5 x - 17$

$x = - 4$

$y = - 5 x - 17$

Step 3

Replace all occurrences of $x$ with $- 4$ in each equation.

Replace all occurrences of $x$ in $y = - 5 x - 17$ with $- 4$ .

$y = - 5 \cdot - 4 - 17$

$x = - 4$

Simplify the right side.

Simplify $- 5 \cdot - 4 - 17$ .

Multiply $- 5$ by $- 4$ .

$y = 20 - 17$

$x = - 4$

Subtract $17$ from $20$ .

$y = 3$

$x = - 4$

$y = 3$

$x = - 4$

$y = 3$

$x = - 4$

$y = 3$

$x = - 4$

Step 4

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

$(- 4, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 4, 3)$

Equation Form:

$x = - 4, y = 3$

Step 6

Solve by Substitution -3x-3y=3 y=-5x-17

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