Find Three Ordered Pair Solutions 6x=-3y+12

$6 x = - 3 y + 12$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $- 3 y + 12 = 6 x$ .

$- 3 y + 12 = 6 x$

Subtract $12$ from both sides of the equation.

$- 3 y = 6 x - 12$

Divide each term in $- 3 y = 6 x - 12$ by $- 3$ and simplify.

Divide each term in $- 3 y = 6 x - 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{6 x}{- 3} + \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{6 x}{- 3} + \frac{- 12}{- 3}$

Divide $y$ by $1$ .

$y = \frac{6 x}{- 3} + \frac{- 12}{- 3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $- 3$ .

Factor $3$ out of $6 x$ .

$y = \frac{3 (2 x)}{- 3} + \frac{- 12}{- 3}$

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y = - 1 \cdot (2 x) + \frac{- 12}{- 3}$

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y = - (2 x) + \frac{- 12}{- 3}$

Multiply $2$ by $- 1$ .

$y = - 2 x + \frac{- 12}{- 3}$

Divide $- 12$ by $- 3$ .

$y = - 2 x + 4$

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.

$y = - 2 \cdot 0 + 4$

Simplify $- 2 \cdot 0 + 4$ .

Multiply $- 2$ by $0$ .

$y = 0 + 4$

Add $0$ and $4$ .

$y = 4$

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

$(0, 4)$

Step 4

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

Remove parentheses.

$y = - 2 \cdot 1 + 4$

Simplify $- 2 \cdot 1 + 4$ .

Multiply $- 2$ by $1$ .

$y = - 2 + 4$

Add $- 2$ and $4$ .

$y = 2$

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

$(1, 2)$

Step 5

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

Remove parentheses.

$y = - 2 \cdot 2 + 4$

Simplify $- 2 \cdot 2 + 4$ .

Multiply $- 2$ by $2$ .

$y = - 4 + 4$

Add $- 4$ and $4$ .

$y = 0$

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

$(2, 0)$

Step 6

These are three possible solutions to the equation.

$(0, 4), (1, 2), (2, 0)$

Step 7

Find Three Ordered Pair Solutions 6x=-3y+12

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