Solve the System of Equations Solve the system of equations 3x+3y=9 and 5x-3y=7 using the Addition Method.

Solve the system of equations $3 x + 3 y = 9$ and $5 x - 3 y = 7$ using the Addition Method.

Solve for $x$ in $3 x + 3 y = 9$ .

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

$3 x = 9 - 3 y$

$5 x - 3 y = 7$

Divide each term in $3 x = 9 - 3 y$ by $3$ and simplify.

Divide each term in $3 x = 9 - 3 y$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3} + \frac{- 3 y}{3}$

$5 x - 3 y = 7$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3} + \frac{- 3 y}{3}$

$5 x - 3 y = 7$

Divide $x$ by $1$ .

$x = \frac{9}{3} + \frac{- 3 y}{3}$

$5 x - 3 y = 7$

$x = \frac{9}{3} + \frac{- 3 y}{3}$

$5 x - 3 y = 7$

$x = \frac{9}{3} + \frac{- 3 y}{3}$

$5 x - 3 y = 7$

Simplify the right side.

Simplify each term.

Divide $9$ by $3$ .

$x = 3 + \frac{- 3 y}{3}$

$5 x - 3 y = 7$

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 3 y$ .

$x = 3 + \frac{3 (- y)}{3}$

$5 x - 3 y = 7$

Cancel the common factors.

Factor $3$ out of $3$ .

$x = 3 + \frac{3 (- y)}{3 (1)}$

$5 x - 3 y = 7$

Cancel the common factor.

$x = 3 + \frac{3 (- y)}{3 \cdot 1}$

$5 x - 3 y = 7$

Rewrite the expression.

$x = 3 + \frac{- y}{1}$

$5 x - 3 y = 7$

Divide $- y$ by $1$ .

$x = 3 - y$

$5 x - 3 y = 7$

$x = 3 - y$

$5 x - 3 y = 7$

$x = 3 - y$

$5 x - 3 y = 7$

$x = 3 - y$

$5 x - 3 y = 7$

$x = 3 - y$

$5 x - 3 y = 7$

$x = 3 - y$

$5 x - 3 y = 7$

$x = 3 - y$

$5 x - 3 y = 7$

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

Replace all occurrences of $x$ in $5 x - 3 y = 7$ with $3 - y$ .

$5 (3 - y) - 3 y = 7$

$x = 3 - y$

Simplify the left side.

Simplify $5 (3 - y) - 3 y$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 3 + 5 (- y) - 3 y = 7$

$x = 3 - y$

Multiply $5$ by $3$ .

$15 + 5 (- y) - 3 y = 7$

$x = 3 - y$

Multiply $- 1$ by $5$ .

$15 - 5 y - 3 y = 7$

$x = 3 - y$

$15 - 5 y - 3 y = 7$

$x = 3 - y$

Subtract $3 y$ from $- 5 y$ .

$15 - 8 y = 7$

$x = 3 - y$

$15 - 8 y = 7$

$x = 3 - y$

$15 - 8 y = 7$

$x = 3 - y$

$15 - 8 y = 7$

$x = 3 - y$

Solve for $y$ in $15 - 8 y = 7$ .

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

Subtract $15$ from both sides of the equation.

$- 8 y = 7 - 15$

$x = 3 - y$

Subtract $15$ from $7$ .

$- 8 y = - 8$

$x = 3 - y$

$- 8 y = - 8$

$x = 3 - y$

Divide each term in $- 8 y = - 8$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 8$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 8}{- 8}$

$x = 3 - y$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 8}{- 8}$

$x = 3 - y$

Divide $y$ by $1$ .

$y = \frac{- 8}{- 8}$

$x = 3 - y$

$y = \frac{- 8}{- 8}$

$x = 3 - y$

$y = \frac{- 8}{- 8}$

$x = 3 - y$

Simplify the right side.

Divide $- 8$ by $- 8$ .

$y = 1$

$x = 3 - y$

$y = 1$

$x = 3 - y$

$y = 1$

$x = 3 - y$

$y = 1$

$x = 3 - y$

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $x = 3 - y$ with $1$ .

$x = 3 - (1)$

$y = 1$

Simplify the right side.

Simplify $3 - (1)$ .

Multiply $- 1$ by $1$ .

$x = 3 - 1$

$y = 1$

Subtract $1$ from $3$ .

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

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

$(2, 1)$

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Solve the System of Equations Solve the system of equations 3x+3y=9 and 5x-3y=7 using the Addition Method.

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