Find Three Ordered Pair Solutions 2x=-6y+4

$2 x = - 6 y + 4$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $- 6 y + 4 = 2 x$ .

$- 6 y + 4 = 2 x$

Subtract $4$ from both sides of the equation.

$- 6 y = 2 x - 4$

Divide each term in $- 6 y = 2 x - 4$ by $- 6$ and simplify.

Divide each term in $- 6 y = 2 x - 4$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{2 x}{- 6} + \frac{- 4}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{2 x}{- 6} + \frac{- 4}{- 6}$

Divide $y$ by $1$ .

$y = \frac{2 x}{- 6} + \frac{- 4}{- 6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $- 6$ .

Factor $2$ out of $2 x$ .

$y = \frac{2 (x)}{- 6} + \frac{- 4}{- 6}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$y = \frac{2 x}{2 \cdot - 3} + \frac{- 4}{- 6}$

Cancel the common factor.

$y = \frac{2 x}{2 \cdot - 3} + \frac{- 4}{- 6}$

Rewrite the expression.

$y = \frac{x}{- 3} + \frac{- 4}{- 6}$

Move the negative in front of the fraction.

$y = - \frac{x}{3} + \frac{- 4}{- 6}$

Cancel the common factor of $- 4$ and $- 6$ .

Factor $- 2$ out of $- 4$ .

$y = - \frac{x}{3} + \frac{- 2 (2)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

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

Cancel the common factor.

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

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 2x=-6y+4

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