Solve by Substitution -3x+3y=3 , -5x+y=13

$- 3 x + 3 y = 3$ , $- 5 x + y = 13$

Step 1

Add $5 x$ to both sides of the equation.

$y = 13 + 5 x$

$- 3 x + 3 y = 3$

Step 2

Replace all occurrences of $y$ with $13 + 5 x$ in each equation.

Replace all occurrences of $y$ in $- 3 x + 3 y = 3$ with $13 + 5 x$ .

$- 3 x + 3 (13 + 5 x) = 3$

$y = 13 + 5 x$

Simplify the left side.

Simplify $- 3 x + 3 (13 + 5 x)$ .

Simplify each term.

Apply the distributive property.

$- 3 x + 3 \cdot 13 + 3 (5 x) = 3$

$y = 13 + 5 x$

Multiply $3$ by $13$ .

$- 3 x + 39 + 3 (5 x) = 3$

$y = 13 + 5 x$

Multiply $5$ by $3$ .

$- 3 x + 39 + 15 x = 3$

$y = 13 + 5 x$

$- 3 x + 39 + 15 x = 3$

$y = 13 + 5 x$

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

$12 x + 39 = 3$

$y = 13 + 5 x$

$12 x + 39 = 3$

$y = 13 + 5 x$

$12 x + 39 = 3$

$y = 13 + 5 x$

$12 x + 39 = 3$

$y = 13 + 5 x$

Step 3

Solve for $x$ in $12 x + 39 = 3$ .

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

Subtract $39$ from both sides of the equation.

$12 x = 3 - 39$

$y = 13 + 5 x$

Subtract $39$ from $3$ .

$12 x = - 36$

$y = 13 + 5 x$

$12 x = - 36$

$y = 13 + 5 x$

Divide each term in $12 x = - 36$ by $12$ and simplify.

Divide each term in $12 x = - 36$ by $12$ .

$\frac{12 x}{12} = \frac{- 36}{12}$

$y = 13 + 5 x$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{- 36}{12}$

$y = 13 + 5 x$

Divide $x$ by $1$ .

$x = \frac{- 36}{12}$

$y = 13 + 5 x$

$x = \frac{- 36}{12}$

$y = 13 + 5 x$

$x = \frac{- 36}{12}$

$y = 13 + 5 x$

Simplify the right side.

Divide $- 36$ by $12$ .

$x = - 3$

$y = 13 + 5 x$

$x = - 3$

$y = 13 + 5 x$

$x = - 3$

$y = 13 + 5 x$

$x = - 3$

$y = 13 + 5 x$

Step 4

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

Replace all occurrences of $x$ in $y = 13 + 5 x$ with $- 3$ .

$y = 13 + 5 (- 3)$

$x = - 3$

Simplify the right side.

Simplify $13 + 5 (- 3)$ .

Multiply $5$ by $- 3$ .

$y = 13 - 15$

$x = - 3$

Subtract $15$ from $13$ .

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

Step 5

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

$(- 3, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, - 2)$

Equation Form:

$x = - 3, y = - 2$

Step 7

Solve by Substitution -3x+3y=3 , -5x+y=13

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