Find Three Ordered Pair Solutions 3x+3y=6

$3 x + 3 y = 6$

Step 1

Solve the equation for $y$ .

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

$3 y = 6 - 3 x$

Divide each term in $3 y = 6 - 3 x$ by $3$ and simplify.

Divide each term in $3 y = 6 - 3 x$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3} + \frac{- 3 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3} + \frac{- 3 x}{3}$

Divide $y$ by $1$ .

$y = \frac{6}{3} + \frac{- 3 x}{3}$

Simplify the right side.

Simplify each term.

Divide $6$ by $3$ .

$y = 2 + \frac{- 3 x}{3}$

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

Factor $3$ out of $- 3 x$ .

$y = 2 + \frac{3 (- x)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = 2 + \frac{3 (- x)}{3 (1)}$

Cancel the common factor.

$y = 2 + \frac{3 (- x)}{3 \cdot 1}$

Rewrite the expression.

$y = 2 + \frac{- x}{1}$

Divide $- x$ by $1$ .

$y = 2 - x$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 2 - (0)$

Subtract $0$ from $2$ .

$y = 2$

Use the $x$ and $y$ values to form the ordered pair.

$(0, 2)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 2 - (1)$

Simplify $2 - (1)$ .

Multiply $- 1$ by $1$ .

$y = 2 - 1$

Subtract $1$ from $2$ .

$y = 1$

Use the $x$ and $y$ values to form the ordered pair.

$(1, 1)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 2 - (2)$

Simplify $2 - (2)$ .

Multiply $- 1$ by $2$ .

$y = 2 - 2$

Subtract $2$ from $2$ .

$y = 0$

Use the $x$ and $y$ values to form the ordered pair.

$(2, 0)$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, 1), (2, 0)$

Step 7

Find Three Ordered Pair Solutions 3x+3y=6

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