Find Three Ordered Pair Solutions 3x=-9y+6

$3 x = - 9 y + 6$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $- 9 y + 6 = 3 x$ .

$- 9 y + 6 = 3 x$

Subtract $6$ from both sides of the equation.

$- 9 y = 3 x - 6$

Divide each term in $- 9 y = 3 x - 6$ by $- 9$ and simplify.

Divide each term in $- 9 y = 3 x - 6$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{3 x}{- 9} + \frac{- 6}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{3 x}{- 9} + \frac{- 6}{- 9}$

Divide $y$ by $1$ .

$y = \frac{3 x}{- 9} + \frac{- 6}{- 9}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ and $- 9$ .

Factor $3$ out of $3 x$ .

$y = \frac{3 (x)}{- 9} + \frac{- 6}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

$y = \frac{3 x}{3 \cdot - 3} + \frac{- 6}{- 9}$

Cancel the common factor.

$y = \frac{3 x}{3 \cdot - 3} + \frac{- 6}{- 9}$

Rewrite the expression.

$y = \frac{x}{- 3} + \frac{- 6}{- 9}$

Move the negative in front of the fraction.

$y = - \frac{x}{3} + \frac{- 6}{- 9}$

Cancel the common factor of $- 6$ and $- 9$ .

Factor $- 3$ out of $- 6$ .

$y = - \frac{x}{3} + \frac{- 3 (2)}{- 9}$

Cancel the common factors.

Factor $- 3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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.

$y = - \frac{0}{3} + \frac{2}{3}$

Simplify $- \frac{0}{3} + \frac{2}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{0 + 2}{3}$

Add $0$ and $2$ .

$y = \frac{2}{3}$

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

$(0, \frac{2}{3})$

Step 4

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

Remove parentheses.

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

Simplify $- \frac{1}{3} + \frac{2}{3}$ .

Combine the numerators over the common denominator.

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

Add $- 1$ and $2$ .

$y = \frac{1}{3}$

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

$(1, \frac{1}{3})$

Step 5

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

Remove parentheses.

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

Simplify $- \frac{2}{3} + \frac{2}{3}$ .

Combine the numerators over the common denominator.

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

Simplify the expression.

Add $- 2$ and $2$ .

$y = \frac{0}{3}$

Divide $0$ by $3$ .

$y = 0$

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

$(2, 0)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{2}{3}), (1, \frac{1}{3}), (2, 0)$

Step 7

Find Three Ordered Pair Solutions 3x=-9y+6

Related Questions

Support LCMGCF.com by disabling your adblocker.